Question

Factorise the following:

5x² – 17x – 12

Answer 1

To factorise 5x² – 17x – 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 5 × –12 = –60 and add up to –17.

These numbers are –20 and 3, because –20 × 3 = –60 and –20 + 3 = –17.

2. Now, rewrite the middle term –17x as –20x + 3x: 5x² – 20x + 3x – 12.

3. Next, factor by grouping (5x² – 20x) + (3x – 12).

4. Factor out the greatest common factor (GCF) from each group: 5x(x – 4) + 3(x – 4).

5. Now, factor out the common binomial factor (x – 4): (5x + 3)(x – 4).

Thus, the factorised form of 5x² – 17x – 12 is (5x + 3) (x – 4).