Question

Factorise the following:

3x² – 5x – 12

Answer 1

To factorise 3x² – 5x – 12, we use the method of splitting the middle term.

Here’s the process:

We want two numbers that multiply to 3 × –12 = –36 and add to –5.

These numbers are –9 and 4 because –9 × 4 = –36 and –9 + 4 = – 5.

Now, we rewrite the middle term –5x as –9x + 4x, giving us 3x² – 9x + 4x – 12.

Next, we factor by grouping (3x² – 9x) + (4x – 12).

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

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

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