Polynomial

An expression of the form a\(_{0}\)x\(^{n}\) + a\(_{1}\)x\(^{n - 1}\) + a\(_{2}\)x\(^{n - 2}\) + a\(_{3}\)x\(^{n - 3}\) + ..... + a\(_{n}\) where a\(_{0}\), a\(_{1}\), a\(_{2}\), a\(_{3}\), ....., a\(_{n}\) are given numbers (real or complex), n is a non-negative integer and x is a variable is called a polynomial in x.

a\(_{0}\), a\(_{1}\), a\(_{2}\), a\(_{3}\), etc., are called the coefficients of x\(^{n}\), x\(^{n - 1}\), x\(^{n - 2}\), x\(^{n - 3}\), etc., respectively.

a\(_{0}\)x\(^{n}\), a\(_{1}\)x\(^{n - 1}\), a\(_{2}\)x\(^{n - 2}\), a\(_{3}\)x\(^{n - 3}\), ....., a\(_{n}\) are called the terms of the polynomial.

a\(_{n}\) is called the constant term. Clearly, it is also the coefficient of x\(^{0}\).

If a\(_{0}\) ≠ 0, the polynomial is said to be of degree n and the term a\(_{0}\)x\(^{n}\) is called the leading term.

The general form of a polynomial of degree 1 is a\(_{0}\)x + a\(_{1}\)where a\(_{0}\) ≠ 0.

The general form of a polynomial of degree 2 is a\(_{0}\)x\(^{2}\) + a\(_{1}\)x + a\(_{2}\) where a\(_{0}\) ≠ 0.

A non-zero constant a\(_{0}\) itself is said to be a polynomial of degree 0 while a polynomial all of whose coefficients are zero is said to be a zero polynomial and is denoted by 0 and no degree is assigned to it.

Since a polynomial is an expression containing the variable x, it is denoted by f(x), p(x) or g(x) etc.

The value of a polynomial f(x) for x = a where a is real number or a complex number is denoted by f(a).

In particular, if the coefficients a\(_{0}\), a\(_{1}\), a\(_{2}\), a\(_{3}\), .... of a polynomial f(x) be all real numbers, the polynomial f(x) is said to be a real polynomial.


Examples of polynomial:

(i) 7x\(^{2}\) + 5x - 3 is a polynomial in x of degree 2 or a quadratic polynomial in x.

(ii) 4x\(^{3}\) + 9x\(^{2}\) - 4x + 2 is a polynomial in x of degree 3 or a cubic polynomial in x.

(iii) 5 - 2x\(^{\frac{5}{3}}\) + 9x\(^{2}\) is an expression but not a polynomial, since it contains a term containing x\(^{\frac{5}{3}}\) , where \(\frac{5}{3}\) is not a non-negative integer. 

● Factorization









10th Grade Math

From Polynomial to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Word Problems on Dividing Money | Solving Money Division Word Problems

    Feb 13, 25 10:29 AM

    Word Problems on Dividing Money
    Read the questions given in the word problems on dividing money. We need to understand the statement and divide the amount of money as ordinary numbers with two digit numbers. 1. Ron buys 15 pens for…

    Read More

  2. Addition and Subtraction of Money | Examples | Worksheet With Answers

    Feb 13, 25 09:02 AM

    Add Money Method
    In Addition and Subtraction of Money we will learn how to add money and how to subtract money.

    Read More

  3. Worksheet on Division of Money | Word Problems on Division of Money

    Feb 13, 25 03:53 AM

    Division of Money Worksheet
    Practice the questions given in the worksheet on division of money. This sheet provides different types of questions on dividing the amount of money by a number; finding the quotient

    Read More

  4. Worksheet on Multiplication of Money | Word Problems | Answers

    Feb 13, 25 03:17 AM

    Worksheet on Multiplication of Money
    Practice the questions given in the worksheet on multiplication of money. This sheet provides different types of questions on multiplying the amount of money by a number; arrange in columns the amount…

    Read More

  5. Division of Money | Worked-out Examples | Divide the Amounts of Money

    Feb 13, 25 12:16 AM

    Divide Money
    In division of money we will learn how to divide the amounts of money by a number. We carryout division with money the same way as in decimal numbers. We put decimal point in the quotient after two pl…

    Read More