]]>
LearnNext
Get a free home demo of LearnNext

Available for CBSE, ICSE and State Board syllabus.
Call our LearnNext Expert on 1800 419 1234 (tollfree)
OR submit details below for a call back

clear

Factorization of Polynomials Using Algebraic Identities

99,404 Views
Have a doubt? Clear it now.
live_help Have a doubt, Ask our Expert Ask Now
format_list_bulleted Take this Lesson Test Start Test

Factorization of Polynomials Using Algebraic Identities - Lesson Summary

Factorisation

If g(x) and h(x) are two polynomials whose product is p(x). This can be written as p(x) = g(x) . h(x). g(x) and h(x) are called the factors of the polynomial p(x).

The process of resolving a given polynomial into factors is called factorisation. A non-zero constant is a factor of every polynomial.

Algebraic Identities

Polynomials can be factorised using algebraic identities.
A polynomial of degree two is called a quadratic polynomial. The identities used to factorise the quadratic polynomials are:

  • (a + b)2 = a2 + 2ab + b2
  • (a – b)2 = a2 – 2ab + b2
  • a2 – b2 = (a + b)(a – b)
  • (x + a)(x + b) = x2 + (a + b)x + ab
  • (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca


A polynomial of degree three is called a cubic polynomial. The algebraic identities used in factorising a cubic polynomial are:

  • (a + b)3 = a3 + b3 + 3ab (a + b)
  • (a – b)3 = a3 – b3 – 3ab (a – b)
  • a3 + b3 = (a + b)(a2 – ab + b2)
  • a3 – b3 = (a – b)(a2 + ab + b2)
  • a3 + b3 + c– 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)

Comments(0)

Feel the LearnNext Experience on App

Download app, watch sample animated video lessons and get a free trial.

Desktop Download Now
Tablet
Mobile
Try LearnNext at home

Get a free home demo. Book an appointment now!

GET DEMO AT HOME