Question

Factorise by substituting terms:

6(x + 2)² – 5(x + 2) – 4

Answer 1

Given expression: 6(x + 2)² – 5(x + 2) – 4

We have to find two numbers whose sum is –5 and whose product is –24.

These numbers are –8 and 3.

Now, using middle term factorisation method,

6(x + 2)² – 5(x + 2) – 4

= 6(x + 2)² – 8(x + 2) + 3(x + 3) – 4

= 2(x + 2) [3(x + 2) – 4] + [3(x + 2) – 4]

= [3(x + 2) – 4] [2(x + 2) + 1]

= (3x + 6 – 4) (2x + 4 + 1)

= (3x + 2) (2x + 5)

The factorisation result is (3x + 2) (2x + 5).