# 9th Class Mathematics Polynomials Polynomials

Polynomials

Category : 9th Class

### Introduction

Previously we have studied about algebraic expression and various operations. In this chapter we will study about a particular types of an algebraic expression, known as polynomials.

### Polynomials

An algebraic expression in which the powers of variable are only non-negative integer.

The general form of a polynomial p(x) of degree n as

$p(x)={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+......+{{a}_{n}}{{x}^{n}}$.

Where ${{a}_{0}},{{a}_{1}},{{a}_{2}}.....{{a}_{n}}$ are constants with ${{a}_{n}}\ne 0$ and n is a non-negative integer.

Degree of Polynomials

The highest power of the variable is called degree of the polynomial.

Find the degree of the following polynomials.

(a) ${{x}^{2}}+7{{x}^{2}}+14{{x}^{6}}+5{{x}^{4}}+5$

Solution:

The degree of polynomial is 6 because the highest power is 6 in $14{{x}^{6}}$.

(b) ${{x}^{2}}y+xy+{{x}^{2}}+x+1$

Solution:

The degree of polynomial is 3 because the highest power is 3 in ${{x}^{2}}y$.

(c) $9{{x}^{3}}+4{{x}^{2}}+4x+5$

Solution:

The degree of polynomial is 3 because the highest power of variable is 3 in $9{{x}^{3}}$.

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