Question

Factorise the following:

10x² + 7x – 12

Answer 1

To factorise 10x² + 7x – 12, we use the method of splitting the middle term.

Here’s the process:

We want two numbers that multiply to 10 × –12 = –120 and add to 7.

These numbers are 15 and –8, because 15 × (–8) = –120 and 15 + (–8) = 7.

Now, we rewrite the middle term 7x and 15x – 8x, giving us 10x² + 15x – 8x – 12.

Next, we factor by grouping (10x² + 15x) – (8x + 12).

Factor out the greatest common factor (GCF) from each group: 5x(2x + 3) – 4(2x + 3).

Now, factor out the common binomial factor (2x + 3) (5x – 4).

Thus, the factorised form of 10x² + 7x – 12 is (2x + 3) (5x – 4).