Question

Write the following as a product of factor: 

x(2x + 1) – 6

Answer 1

x(2x + 1) – 6 = 2x² + x – 6

We have to find two numbers whose sum is 1 and whose product is –12. 

These numbers are 4 and –3.

Now, using middle term factorisation method,

2x² + x – 6

= 2x² + 4x – 3x – 6

= 2x(x + 2) – (3x + 2)

= (x + 2) (2x – 3)

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