Question

Factorise the following:

x² – 18x – 63

Answer 1

Given expression: x² – 18x – 63

Step-wise calculation:

1. Identify two numbers whose product is –63 the constant term and whose sum is –18 the coefficient of x.

2. The pair of numbers that satisfies this is –21 and 3 because:

–21 × 3 = –63 and –21 + 3 = –18

3. Rewrite the middle term –18x as –21x + 3x:

x² – 21x + 3x – 63

4. Factor by grouping:

(x² – 21x) + (3x – 63)

= x(x – 21) + 3(x – 21)

5. Factor out the common binomial factor (x – 21):

(x + 3)(x – 21)