Polynomials are algebraic expressions that consist of variables and coefficients. The addition, subtraction and multiplication of polynomials P and Q result in a polynomial where. Also, register now to access numerous video lessons for different math concepts to learn in a more effective and engaging way. Greatest Common Factor. Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms". To divide polynomials, follow the given steps: If a polynomial has more than one term, we use long division method for the same. To add polynomials, always add the like terms, i.e. that can be combined using addition, subtraction, multiplication and division ... A polynomial can have constants, variables and exponents, Polynomial P(x) is divisible by binomial (x – a) if and only if P(a) = 0. Example: x4 − 2x2 + x has three terms, but only one variable (x), Example: xy4 − 5x2z has two terms, and three variables (x, y and z). The addition of polynomials always results in a polynomial of the same degree. The highest degree is 6, so that goes first, then 3, 2 and then the constant last: You don't have to use Standard Form, but it helps. E-learning is the future today. Let us now consider two polynomials, P (x) and Q (x). The standard form of writing a polynomial equation is to put the highest degree first then, at last, the constant term. How To: Given a polynomial function [latex]f[/latex], use synthetic division to find its zeros. Time Complexity: O (m + n) where m and n are number of nodes in first and second lists respectively. A few examples of trinomial expressions are: Some of the important properties of polynomials along with some important polynomial theorems are as follows: If a polynomial P(x) is divided by a polynomial G(x) results in quotient Q(x) with remainder R(x), then. Example: x 4 −2x 2 +x. allowing for multiplicities, a polynomial function will have the same number of factors as its degree, and each factor will be in the form \((x−c)\), where \(c\) is a complex number. Examples of … Every non-constant single-variable polynomial with complex coefficients has at least one complex root. The division of two polynomials may or may not result in a polynomial. Get NCERT Solutions for Class 5 to 12 here. Polynomial Identities : An algebraic expression in which the variables involved have only non negative integral powers is called polynomial. Storing Polynomial in a Linked List . Coefficients : In the polynomial coefficient of respectively and we also say that +1 is the constant term in it. Name Space Year Rating. Polynomial Identities. Determine the area and volume of geometrical shapes and unknown constants in the polynomial equations too. Post navigation ← Implementation of queue using singly linked list Library management Software → The Chebyshev polynomials are two sequences of polynomials related to the sine and cosine functions, notated as T n (x) and U n (x).They can be defined several ways that have the same end result; in this article the polynomials are defined by starting with trigonometric functions: . A polynomial p (x) is the expression in variable x which is in the form (ax n + bx n-1 + …. Q (x)=8x+6. Instead of saying "the degree of (whatever) is 3" we write it like this: When Expression is a Fraction. +x-12. Repeat step 2 to 4 until you have no more terms to carry down. Select the correct answer and click on the “Finish” buttonCheck your score and answers at the end of the quiz, Visit BYJU’S for all Maths related queries and study materials, I am doing algebra at school , and I forgot alot about it. Then, equate the equation and perform polynomial factorization to get the solution of the equation. See how nice and smooth the curve is? Definition, degree and names; Evaluating polynomials; Polynomials Operations. The word polynomial is derived from the Greek words ‘poly’ means ‘many‘ and ‘nominal’ means ‘terms‘, so altogether it said “many terms”. While a polynomial can include constants such as 3, -4 or 1/2, variables, which are often denoted by letters, and exponents, there are two things polynomials can't include. (Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!). Solve these using mathematical operation. Affine fixed-point free … Introduction. Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). Then solve as basic algebra operation. … Keep visiting BYJU’S to get more such math lessons on different topics. a polynomial function with degree greater than 0 has at least one complex zero. but those names are not often used. Hence. For example, in a polynomial, say, 2x2 + 5 +4, the number of terms will be 3. Description. To add polynomials, always add the like terms, i.e. the terms having the same variable and power. If P(x) is divided by (x – a) with remainder r, then P(a) = r. A polynomial P(x) divided by Q(x) results in R(x) with zero remainders if and only if Q(x) is a factor of P(x). Let us study below the division of polynomials in details. Combining like terms; Adding and subtracting; … An example of a polynomial with one variable is x2+x-12. Based on the numbers of terms present in the expression, it is classified as monomial, binomial, and trinomial. The division of polynomials is an algorithm to solve a rational number which represents a polynomial divided by a monomial or another polynomial. The largest degree of those is 4, so the polynomial has a degree of 4. If the remainder is 0, the candidate is a zero. Polynomial addition, multiplication (8th degree polynomials) using arrays #include #include #include #define MAX 17 void init(int p[]); void read(int p[]); void print(int p[]); void add(int p1[],int p2[],int p3[]); void multiply(int p1[],int p2[],int p3[]); /*Polynomial is stored in an array, p[i] gives coefficient of x^i . The degree of a polynomial with only one variable is the largest exponent of that variable. The cubic polynomial f(x) = 4x3 − 3x2 − 25x − 6 has degree `3` (since the highest power of x … therefore I wanna some help, Your email address will not be published. We can perform arithmetic operations such as addition, subtraction, multiplication and also positive integer exponents for polynomial expressions but not division by variable. This entry was posted in C Programming and tagged c program, evaluation Polynomial, Implementation, linked list on December 20, 2011 by Rajesh Hegde. First, isolate the variable term and make the equation as equal to zero. The number of positive real zeroes in a polynomial function P(x) is the same or less than by an even number as the number of changes in the sign of the coefficients. A polynomial thus may be represented using arrays or linked lists. A term is made up of coefficient and exponent. Writing it Down. Example: Find the difference of two polynomials: 5x3+3x2y+4xy−6y2, 3x2+7x2y−2xy+4xy2−5. If P(x) is a polynomial with real coefficients and has one complex zero (x = a – bi), then x = a + bi will also be a zero of P(x). These multiplying polynomials worksheets with answer keys encompass polynomials to be multiplied by monomials, binomials, trinomials and polynomials; involving single and multivariables. but never division by a variable. an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable). The terms of polynomials are the parts of the equation which are generally separated by “+” or “-” signs. the terms having the same variable and power. \(x^3 + 3x^2y^4 + 4y^2 + 6\) We follow the above steps, with an additional step of adding the powers of different variables in the given terms. They are Monomial, Binomial and Trinomial. Thus, the degree of the polynomial will be 5. We can work out the degree of a rational expression (one that is in the form of a fraction) by taking the degree of the top (numerator) and subtracting the degree of the bottom (denominator). The polynomials arise in: probability, such as the Edgeworth series;; in combinatorics, as an example of an Appell sequence, obeying the umbral calculus;; in numerical analysis as Gaussian quadrature;; in physics, where they give rise to the eigenstates of the quantum harmonic … This is because in \(3x^2y^4\), the exponent values of x and y are 2 and 4 respectively. Now subtract it and bring down the next term. Examples of constants, variables and exponents are as follows: The polynomial function is denoted by P(x) where x represents the variable. a polynomial 3x^2 + … Your email address will not be published. It is possible to subtract two polynomials, each of degree 4, and have the difference be a polynomial of degree 3. For an expression to be a monomial, the single term should be a non-zero term. In this chapter, we will learn the concept of dividing polynomials, which is slightly more detailed than multiplying them. Covid-19 has led the world to go through a phenomenal transition . For example, If the variable is denoted by a, then the function will be P(a). The explanation of a polynomial solution is explained in two different ways: Getting the solution of linear polynomials is easy and simple. Also, polynomials of one variable are easy to graph, as they have smooth and continuous lines. So, each part of a polynomial in an equation is a term. Visit us for detailed chapter-wise solutions of NCERT, RD Sharma, RS Agrawal and more prepared by our expert faculties at Toppr. If a polynomial P is divisible by a polynomial Q, then every zero of Q is also a zero of P. If a polynomial P is divisible by two coprime polynomials Q and R, then it is divisible by (Q • R). For more complicated cases, read Degree (of an Expression). GGiven two polynomial numbers represented by a circular linked list, the task is to add these two polynomials by adding the coefficients of the powers of the same variable. Polynomials are of 3 different types and are classified based on the number of terms in it. Polynomial Addition: (7s3+2s2+3s+9) + (5s2+2s+1), Polynomial Subtraction: (7s3+2s2+3s+9) – (5s2+2s+1), Polynomial Multiplication:(7s3+2s2+3s+9) × (5s2+2s+1), = 7s3 (5s2+2s+1)+2s2 (5s2+2s+1)+3s (5s2+2s+1)+9 (5s2+2s+1)), = (35s5+14s4+7s3)+ (10s4+4s3+2s2)+ (15s3+6s2+3s)+(45s2+18s+9), = 35s5+(14s4+10s4)+(7s3+4s3+15s3)+ (2s2+6s2+45s2)+ (3s+18s)+9, Polynomial Division: (7s3+2s2+3s+9) ÷ (5s2+2s+1). smooth the curve is? We need to add the coefficients of variables with the same power. The list contains polynomials of degree 2 to 32. There are special names for polynomials with 1, 2 or 3 terms: How do you remember the names? An example of a polynomial equation is: A polynomial function is an expression constructed with one or more terms of variables with constant exponents. Subtracting polynomials is similar to addition, the only difference being the type of operation. Below is the list of all families of symmetric functions and related families of polynomials currently covered. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial. Array representation assumes that the exponents of the given expression are arranged from 0 to the … This cannot be simplified. So, if there are “K” sign changes, the number of roots will be “k” or “(k – a)”, where “a” is some even number. To find the degree of the given polynomial, combine the like terms first and then arrange it in ascending order of its power. Examples: Input: 1st Number = 5x^2 * y^1 + 4x^1 * y^2 + 3x^1 * y^1 + 2x^1 2nd Number = 3x^1 * y^2 + 4x^1 In a linked list node contains 3 members, coefficient value link to the next node. 1st Number: 5x^2+4x^1+2x^0 2nd Number: -5x^1-5x^0 Added polynomial: 5x^2-1x^1-3x^0. we will define a class to define polynomials. Therefore, division of these polynomial do not result in a Polynomial. A few examples of binomials are: A trinomial is an expression which is composed of exactly three terms. Mathematically, upon adding the two expressions, we would get the resultant polynomial, R (x)=6x 2 +15x+10. Related Article: Add two polynomial numbers using Arrays. The Standard Form for writing a polynomial is to put the terms with the highest degree first. Division of two polynomial may or may not result in a polynomial. Use the answer in step 2 as the division symbol. The following is a list of primitive irreducible polynomials for generating elements of a binary extension field GF(2 m) from a base finite field. First, combine the like terms while leaving the unlike terms as they are. For a Multivariable Polynomial. A Polynomial can be expressed in terms that only have positive integer exponents and the operations of addition, subtraction, and multiplication. Polynomials are algebraic expressions that consist of variables and coefficients. To create a polynomial, one takes some terms and adds (and subtracts) them together. P(x) = 4x 3 +6x 2 +7x+9. In other words, it must be possible to write the expression without division. Find the Degree of this Polynomial: 5x 5 +7x 3 +2x 5 +9x 2 +3+7x+4. First, arrange the polynomial in the descending order of degree and equate to zero. So, 5x 5 +7x 3 +2x 5 +9x 2 +3+7x+4 = 7x 5 + 7x 3 + 9x 2 + 7x + 7. In this example, there are three terms: x, The word polynomial is derived from the Greek words ‘poly’ means ‘. The Chebyshev polynomials of the first kind (T n) are given by T n (cos(θ) ) = cos(n θ). Learn about degree, terms, types, properties, polynomial functions in this article. Variables are also sometimes called indeterminates. So you can do lots of additions and multiplications, and still have a polynomial as the result. Index of polynomials. A monomial is an expression which contains only one term. A few examples of monomials are: A binomial is a polynomial expression which contains exactly two terms. + jx+ k), where a, b, c …., k fall in the category of real numbers and 'n' is non negative integer, which is called the degree of polynomial. Following are the steps for it. In general, there are three types of polynomials. Click ‘Start Quiz’ to begin! An example to find the solution of a quadratic polynomial is given below for better understanding. Example: The Degree is 3 (the largest … Linear Factorization Theorem. There is also quadrinomial (4 terms) and quintinomial (5 terms), Basics of polynomials. If P(x) = a0 + a1x + a2x2 + …… + anxn is a polynomial such that deg(P) = n ≥ 0 then, P has at most “n” distinct roots. Make a polynomial abstract datatype using struct which basically implements a linked list. Put your understanding of this concept to test by answering a few MCQs. Also, polynomials of one variable are easy to graph, as they have smooth and continuous lines. You can also divide polynomials (but the result may not be a polynomial). Rational Zero Theorem For adding two polynomials that are stored as a linked list. While solving the polynomial equation, the first step is to set the right-hand side as 0. Check the highest power and divide the terms by the same. Note the final answer, including remainder, will be in the fraction form (last subtract term). In this example, there are three terms: x2, x and -12. \(\text{If }{{x}^{2}}+\frac{1}{{{x}^{2}}}=27,\text{ find the value of the }x-\frac{1}{x}\) Solution: We … The three types of polynomials are: These polynomials can be combined using addition, subtraction, multiplication, and division but is never division by a variable. A polynomial can have any number of terms but not infinite. Next to each link is the vector space where they live, year when they were introduced, and my personal judgement of how much information I have managed to write down about the family. Division of polynomials Worksheets. Example: Find the degree of the polynomial 6s4+ 3x2+ 5x +19. The classification of a polynomial is done based on the number of terms in it. If we take a polynomial expression with two variables, say x and y. Given two polynomial 7s3+2s2+3s+9 and 5s2+2s+1. 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Degree. Representation of a Polynomial: A polynomial is an expression that contains more than two terms. An example of finding the solution of a linear equation is given below: To solve a quadratic polynomial, first, rewrite the expression in the descending order of degree. So, subtract the like terms to obtain the solution. A binomial can be considered as a sum or difference between two or more monomials. Also, x2 – 2ax + a2 + b2 will be a factor of P(x). submit test. It should be noted that subtraction of polynomials also results in a polynomial of the same degree. Degree of a polynomial in one variable : In case of a polynomial in one variable the highest power of the variable is called the degree of … A few examples of Non Polynomials are: 1/x+2, x-3. The first method for factoring polynomials will be factoring out the … For factorization or for the expansion of polynomial we use the following … Use synthetic division to evaluate a given possible zero by synthetically dividing the candidate into the polynomial. Note: In given polynomials, the term containing the higher power of x will come first. The degree of a polynomial is defined as the highest degree of a monomial within a polynomial. In the polynomial linked list, the coefficients and exponents of the polynomial are defined as the data node of the list. This article is contributed by Akash Gupta. But, when we represent these polynomials in singly linked list, it would look as below: The best option for storing polynomials is a linear linked list to store terms of the polynomials and perform its operations like addition, subtraction or multiplication. If you have been to highschool, you will have encountered the terms polynomial and polynomial function.This chapter of our Python tutorial is completely on polynomials, i.e. If there are real numbers denoted by a, then function with one variable and of degree n can be written as: Any polynomial can be easily solved using basic algebra and factorization concepts. You can also divide polynomials (but the result may not be a polynomial). Example: 21 is a polynomial. It's easiest to understand what makes something a polynomial equation by looking at examples and non examples as shown below. The polynomial equations are those expressions which are made up of multiple constants and variables. Here is a typical polynomial: Two or more polynomial when multiplied always result in a polynomial of higher degree (unless one of them is a constant polynomial). The other two are the Laguerre polynomials, which are orthogonal over the half line [, ∞), and the Hermite polynomials, orthogonal over the full line (− ∞, ∞), with weight functions that are the most natural analytic functions that ensure convergence of all integrals. Primitive Polynomial List. The second forbidden element is a negative exponent because it amounts to division by a variable. Polynomials : An algebraic expression in which the variables involved have only nonnegative integral powers is called a polynomial. It has just one term, which is a constant. The addition of polynomials always results in a polynomial of the same degree. Think cycles! For example, x. Because of the strict definition, polynomials are easy to work with. An example of multiplying polynomials is given below: ⇒ 6x ×(2x+5y)–3y × (2x+5y) ———- Using distributive law of multiplication, ⇒ (12x2+30xy) – (6yx+15y2) ———- Using distributive law of multiplication. The degree of a polynomial with only one variable is the largest exponent of that variable. Stay Home , Stay Safe and keep learning!!! … For example, 3x, A standard polynomial is the one where the highest degree is the first term, and subsequently, the other terms come. For example, Example: Find the sum of two polynomials: 5x3+3x2y+4xy−6y2, 3x2+7x2y−2xy+4xy2−5. Polynomials with odd degree always have at least one real root? P (x)=6x 2 +7x+4. polynomial addition using linked list in c,program for polynomial addition using linked list in data structure in c,addition of two polynomials using circular linked list in c,polynomial subtraction using linked list,polynomial addition and subtraction using linked list in c,polynomial division using linked list in c, Also they can have one or more terms, but not an infinite number of terms. There are four main polynomial operations which are: Each of the operations on polynomials is explained below using solved examples. Use the Rational Zero Theorem to list all possible rational zeros of the function. We write different functions for Creating (ie, adding more nodes to the linked list) a polynomial function, Adding two polynomials and Showing a polynomial expression. Carry down coefficients has at least one real root learn in a polynomial is. Wan na some help, your email address will not be published polynomial of higher (... How do you remember the names all possible rational zeros of the polynomial equation is Fraction! Polynomial P ( a ) the degree of a polynomial abstract datatype struct. Polynomial factorization to get the solution 5 '' is a polynomial equation the! ( last subtract term ) three terms: how do you remember the?! Term should be a polynomial, one term: When expression is polynomial. Polynomial can have one or more polynomial When multiplied always result in a polynomial where 5 +4 the. Variable are easy to work with be P ( a ) = 0 the! The second forbidden element is a constant to graph, as they have smooth and continuous lines polynomials! 4 terms ), but those names are not often used other words, it be... Polynomial where the right-hand side as 0: When expression is list of polynomials Fraction degree a! For adding two polynomials may or may not be published the coefficients of with! Be 5 dividing the candidate into the polynomial will be a factor of P a! Coefficient of respectively and we also say that +1 is the list of all families of.. Not result in a polynomial expression with two variables, say, 2x2 + +4. Help, your email address will not be a factor of P ( x ) and Q result a! Exactly three terms “ terms. ” ) + 5 +4, the constant term in it 5x.! Then arrange it in ascending order of its power polynomial of degree and names ; Evaluating polynomials ; operations! Subtracting polynomials is explained below using solved examples not an infinite number terms! The polynomial equations too terms in it is 0, the Hermite polynomials are: a polynomial is.... Polynomials with 1, 2 or 3 terms: x2, x and y degree... Using solved examples a trinomial is an expression which contains only one variable denoted! Lessons on different topics arrays or linked lists in first and second lists respectively on the numbers of in! Find its zeros terms ), but not infinite ( 3x^2y^4\ ), the term containing the power... Equations are those expressions which are made up of multiple constants and variables for example, are... Constant! ) terms will be 5 polynomial Identities: an algebraic expression which! Terms while leaving the unlike terms as they have smooth and continuous lines, including remainder will... Are special names for polynomials with 1, 2 or 3 terms: x2, x and y 2... Is called a degree of the polynomial equation, the exponent values of x will come first negative. Non-Zero term largest … Primitive polynomial list the only difference being the type operation. Of a monomial is an algorithm to solve a rational number which represents polynomial... Say, 2x2 + 5 +4, the term containing the higher power of x and y are and! Monomial, binomial, and multiplication of these polynomial do not result in polynomial. The solution polynomials that are stored as a sum or difference between two or more polynomial When multiplied result! +6X 2 +7x+9, binomial, and still have a polynomial of non polynomials are algebraic expressions that consist variables... Easy and simple final answer, including remainder, will be in the polynomial will be.... “ - ” signs amounts to division by a variable, so an expression ) 2 +7x+9 be in! Will be in the expression without division area and volume of geometrical shapes and unknown constants in the expression it... Us study below the division of polynomials also results in a linked Library... ” ) saying `` the degree of a polynomial equation having one variable which has the largest … Primitive list! ) = 4x 3 +6x 2 +7x+9 be represented using arrays be in the Fraction form ( last subtract )! Complex root and related families of symmetric functions and related families of symmetric functions and related of! Polynomial: 5x^2-1x^1-3x^0 make the equation which are generally separated by “ + ” “! Expression, it is possible to subtract two polynomials may or may result! Can also divide polynomials ( but the result may not result in a linked list Library management →! So, each part of a polynomial divided by a variable, so an expression which is a polynomial within. Side as 0 the Fraction form ( last subtract term ) of variable! Within a polynomial can have one or more polynomial When multiplied always in. ) =6x 2 +15x+10! ) may or may not be published [ /latex ] use! Algebraic expression in which the variables involved have only non negative integral powers is called.... Determine the area and volume of geometrical shapes and unknown constants in the polynomial be. Are generally separated by “ + ” or “ - ” signs in other words, is! Binomials are: 1/x+2, x-3 are stored as a linked list Library management Software → Index of polynomials explained. Are special names for polynomials with 1, 2 or 3 terms: x2, x and.... Us study below the division of polynomials P and Q ( x ) =.! Complex list of polynomials has at least one real root first then, at,! Have one or more polynomial When multiplied always result in a polynomial of the operations of,. Will learn the concept of dividing polynomials, always add the like terms first second... Types, properties, polynomial functions in this Article – 2ax + a2 + b2 will be P ( )! ( m + n ) where m and n are number of terms but not.. ( meaning “ many ” ) and Nominal ( meaning “ terms. ” ) and Nominal ( meaning many. Now consider two polynomials, each part of a monomial or another polynomial of coefficient and.. More detailed than multiplying them with two variables, say x and y are and... Of NCERT, RD Sharma, RS Agrawal and more prepared by our expert faculties at Toppr polynomials... Which the variables involved have only non negative integral powers is called polynomial all possible rational zeros of same... 3X2+ 5x +19 equations too! ), as they are the solution of the strict definition, polynomials degree... Within a polynomial abstract datatype using struct which basically implements a linked list node 3. [ latex ] f [ /latex ], use synthetic division to evaluate a given possible by! First, isolate the variable is denoted by a variable repeat step 2 as the division two... Polynomials ; polynomials operations, RD Sharma, RS Agrawal and more prepared by expert... Will come first form for writing a polynomial is defined as the result, equate the equation and perform factorization., it is possible to subtract two polynomials that are stored as a linked list node 3... The solution of linear polynomials is similar to addition, subtraction and multiplication, `` 5 '' is constant... An example of a quadratic polynomial is defined as the highest degree of the polynomial contains a term allowed... Rational number which represents a polynomial, one term is made up of two polynomials or., including remainder, will be P ( a ) = 4x 3 +6x 2 +7x+9 by... Lessons list of polynomials different topics the names polynomial equation, the number of terms When multiplied always in. Unlike terms as they have smooth and continuous lines polynomials may or not! More than two terms first and second lists respectively similar to addition subtraction... \ ( 3x^2y^4\ ), the candidate into the polynomial 6s4+ 3x2+ 5x +19 properties, polynomial in... Single-Variable polynomial with only one variable are easy to work with coefficient of respectively and we also say +1! The largest exponent of that variable equation is to put the highest power and the... Higher power of x and y are 2 and 4 respectively + +! Say, 2x2 + 5 +4, the candidate into the polynomial equations too latex ] f /latex. A sum or difference between two or more polynomial When multiplied always result in polynomial..., register now to access numerous video lessons for different math concepts to learn in polynomial. The coefficients of variables with the highest degree first us study below the division two. They have smooth and continuous lines different math concepts to learn in a linked list 3. Always results in a polynomial of the same power coefficients of variables coefficients. As the result may not be published in first and second lists respectively a sum or difference between two more. All possible rational zeros of the same degree datatype using struct which basically implements a list! 5 + 7x 3 + 9x 2 + 7x 3 + 9x +! Are algebraic expressions that consist of variables and coefficients “ + ” or “ - ” signs order... Because it amounts to division by a monomial or another polynomial 3 ( the largest exponent is called a of! Would get the resultant polynomial, R ( x ) is divisible by binomial ( x ):... 3 terms: how do you remember the names having one variable are easy work. Terms by the same degree of degree and names ; Evaluating polynomials polynomials. Coefficients of variables and coefficients /latex ], use synthetic division to find its zeros contains! N are number of terms present in the polynomial coefficient of respectively we!