# Factorization of Cubic Polynomial

Covid-19 has led the world to go through a phenomenal transition .

E-learning is the future today.

Stay Home , Stay Safe and keep learning!!!

In this section, we will discuss Factorization of Cubic Polynomial.

The degree of the cubic (highest exponent) polynomial is 3.
There are different identities in Factorization of Cubic Polynomial .
They are as follows :
1) a3 + b3 + 3a2b + 3b2a = (a + b)3

2) a3 - b3 - 3a2b + 3b2a = (a - b)3

3) a3 + b3 = (a + b)(a2 - ab + b2)

4) a3- b3 = (a - b)(a2 + ab + b2)

5) a3 + b3+ c3- 3abc
= (a + b + c)(a2 + b2+ c2 - ab - bc - ac)

6) If a + b + c = 0 then a3 + b3+ c3=3abc

Using Identities

Examples :

1)27x3- 8

Solution :
As first term and the 2nd term are perfect cube, we use the identity of cube

 (a3 - b3) = ( a - b)(a2 +ab + b2)

a = 3x and b = 2

27x3- 8 = (3x -2)[(3x)2 + 6x + 22)]

= (3x -2)(9x2 + 6x + 4)are the factors.

________________________________________________________________
2) 8x3 +1

Solution :
As first term and the 2nd term are perfect cube, we use the identity of cube

 (a3 + b3) = ( a + b)(a2 -ab + b2)

a = 2x and b = 1

8x3+ 1 = (2x + 1)[(2x)2 - 2x + 12)]

= (2x +1 )(4x2 - 2x + 1)are the factors.

________________________________________________________________
3) 27x3 + y3 + 9x2y + 3xy2

Solution :
As in the given equation there are two perfect cubes, so we can use 1st identity.

27x3 + y3 + 27x2y + 9xy2

= (3x)3 + (y)3 + 3(3x)2y + 3(3x)y2

= (3x + y)3 [ here a = 3x and b= y;a3 + b3 + 3a2b + 3b2a = (a + b)3 ]

_______________________________________________________________
4) (1.5)3 - (0.9)3 - (0.6)3

Solution :
(1.5)3 - (0.9)3 + (-0.6)3

Let a = 1.5, b = - 0.9 and c = -0.6

As a + b + c = 1.5 + 0.9 - 0.6 = 0

a3 + b3+ c3 = 3abc

= 3(1.5)(- 0.9)(-0.6)

= 2.430

Factoring

Factorization by common factor
Factorization by Grouping
Factorization using Identities
Factorization of Cubic Polynomial
Solved Examples on Factorization