2.2 Factorisation of Quadratic Expression

2.2 Factorisation of Quadratic Expression

(A) Factorisation quadratic expressions of the form
       ax2 + bx + c, b = 0 or c = 0
1. Factorisation of quadratic expressions is a process of finding two linear expressions whose product is the same as the quadratic expression.
2. Quadratic expressions ax2 + c and ax2 + bx that consist of two terms can be factorised by finding the common factors for both terms.

Example 1:
Factorise each of the following:
(a) 2x2 + 6
(b) 7p2 – 3p
(c) 6x2 – 9x

Solution:
(a) 2x2 + 6 = 2 (x2 + 3) ← (2 is common factor)
(b) 7p2 – 3p = p (7p – 3) ← (p is common factor)
(c) 6x2 – 9x = 3x (2x – 3) ← (3x is common factor)


(B) Factorisation of quadratic expressions in the form ax2c , where a and c are perfect squares

Example 2:
(a) 9p2 – 16
(b) 25x2 – 1
(c) 1 4 1 25 x 2

Solution: 
(a) 9p2 – 16 = (3p)2 – 42 = (3p – 4) (3p + 4)
(b) 25x2 – 1 = (5x)2 – 12 = (5x – 1) (5x + 1)
(c)
1 4 1 25 x 2 = ( 1 2 ) 2 ( 1 5 x ) 2               =( 1 2 1 5 x )( 1 2 + 1 5 x )


(C) Factorisation quadratic expressions in the form ax2 + bx + c, where a ≠ 0, b ≠ 0 and c ≠ 0

Example 3:
Factorise each of the following
(a) 3y2 + 2y – 8
(b) 4x2 – 12x + 9

Solution: 
(a)
Factorise using the Cross Method


3y2 + 2y – 8 = (3y – 4) (y + 2)
(b)


4x2 – 12x + 9 = (2x – 3) (2x – 3)