Question

Factorise the following:

x² + 10x – 24

Answer 1

Given expression: x² + 10x – 24

Step-wise calculation:

1. We look for two numbers whose product is the constant term –24 and whose sum is the coefficient of the middle term +10.

2. Factors of –24 that add up to 10 are 12 and –2 because 12 × –2 = –24 and 12 + (–2) = 10.

3. Rewrite the middle term using these numbers:

x² + 12x – 2x – 24

4. Group terms:

(x² + 12x) + (–2x – 24)

5. Factor each group:

x(x + 12) – 2(x + 12)

6. Factor out the common binomial:

(x + 12)(x – 2)