Question

Factorise the following:

4x² – 8x – 21

Answer 1

To factorise 4x² – 8x – 21, we use the method of splitting the middle term.

Here’s the step-by-step process:

1. We need to find two numbers that multiply to 4 × –21 = –84 and add up to –8 (the coefficient of x).
   These numbers are –14 and 6, because –14 × 6 = –84 and –14 + 6 = –8.
2. Now, rewrite the middle term –8x as –14x + 6x: 4x² – 14x + 6x – 21.
3. Next, factor by grouping (4x² – 14x) + (6x – 21).
4. Factor out the greatest common factor (GCF) from each group: 2x(2x – 7) + 3(2x – 7).
5. Now, factor out the common binomial factor (2x – 7): (2x + 3)(2x – 7).
   Thus, the factorised form of 4x² – 8x – 21 is (2x + 3) (2x – 7).