Question

Factorise the following:

2x² – 3x – 65

Answer 1

To factorise 2x² – 3x – 65, 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 2 × –65 = –130 and add up to –3 (the coefficient of x).
   These numbers are –13 and 10, because –13 × 10 = –130 and –13 + 10 = –3.
2. Now, rewrite the middle term –3x as –13x + 10x: 2x² – 13x + 10x – 65.
3. Next, factor by grouping (2x² – 13x) + (10x – 65).
4. Factor out the greatest common factor (GCF) from each group: x(2x – 13) + 5(2x – 13).
5. Now, factor out the common binomial factor (2x – 13): (x + 5)(2x – 13).
6. Thus, the factorised form of 2x² – 3x – 65 is (x + 5) (2x – 13).