Question

Factorise the following:

6x² – x – 12

Answer 1

To factorise 6x² – x – 12, we use the method of splitting the middle term.

Here’s the step-by-step process:

1. We want to find two numbers that multiply to 6 × –12 = –72 and add up to –1 (the coefficient of x).
   These numbers are –9 and 8, because –9 × 8 = –72 and –9 + 8 = –1.
2. Now, rewrite the middle term –x as –9x + 8x: 6x² – 9x + 8x – 12.
3. Next, factor by grouping (6x² – 9x) + (8x – 12).
4. Factor out the greatest common factor (GCF) from each group: 3x(2x – 3) + 4(2x – 3).
5. Now, factor out the common binomial factor (2x – 3): (3x + 4)(2x – 3).
   Thus, the factorised form of 6x² – x – 12 is (3x + 4) (2x – 3).