Polynomials Summary

Polynomial

An algebraic expression of the form a₀+a₁x+a₂x²+….+a_nxⁿ where

a₀, a₁, a₂,….a_n are real numbers, n is a positive integer is called a polynomial in x.

Methods of factorising polynomials

There are various methods of factorising a polynomial. They are,

Factorisation by dividing the expression by the HCF of the terms of

the given expression.

Factorisation by grouping the terms of the expression.

Factorisation using identities.

Remainder theorem

If f(x) is a polynomial in x and is divided by x-a; then the remainder is

is the value of f(x) at x = a i.e., remainder = f(a).

Factor theorem

If p(x) is a polynomial in x and is divided by and the remainder = f(a) is zero then (x-a) is a factor of p(x).