9th Class Mathematics Polynomials Polynomials

         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 \[9{{x}^{3}}\].