Question

Factorise the following:

x² – 5x – 50

Answer 1

Given expression: x² – 5x – 50

Step-wise calculation:

1. Find two numbers whose product is –50 and whose sum is –5.

Factors of –50 are –10 × 5 = –50

Sum: –10 + 5 = –5

2. Rewrite the middle term –5x as –10x + 5x:

x² – 10x + 5x – 50

3. Group terms:

(x² – 10x) + (5x – 50)

4. Factor each group:

x(x – 10) + 5(x – 10)

5. Factor out the common binomial factor (x – 10):

(x – 10)(x + 5)