Class 9 · Chapter 2

Polynomials

Degree, zeroes, Remainder theorem, Factor theorem, algebraic identities and factorisation.

Watch this chapter

Read the full chapter

Tip: open the NCERT PDF for the original chapter text alongside the notes here.

Detailed theory

A polynomial in

x

p(x) = a_n x^n + a_{n-1}x^{n-1} + \ldots + a_1 x + a_0

where

a_i

are real and

n

is a non-negative integer. The largest

n

with

a_n \ne 0

is the degree. Constants (non-zero) have degree

0

; the zero polynomial has no degree.

Key concepts & formulas

Degree of a polynomial

=

highest power of the variable.

(x - a)

is a factor of

p(x)

iff

p(a) = 0

(a+b)^2 = a^2 + 2ab + b^2

;

(a-b)^2 = a^2 - 2ab + b^2

(a+b)^3 = a^3 + b^3 + 3ab(a+b)

;

(a-b)^3 = a^3 - b^3 - 3ab(a-b)

a^3 + b^3 = (a+b)(a^2 - ab + b^2)

;

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

Remainder theorem: dividing

p(x)

(x-a)

leaves remainder

p(a)