Question

Factorise the following:

x² – 27x + 180

Answer 1

Given: x² – 27x + 180

Step-wise calculation:

1. We want to factorise the quadratic expression x² – 27x + 180 into the form (x – a)(x – b), where a and b satisfy two conditions:

a + b = 27 the coefficient of x but positive because of the minus sign in the expression a × b = 180.

2. Find two numbers a and b such that

a + b = 27 and a × b = 180

3. By testing factor pairs of 180:

9 + 20 = 29 not 27

12 + 15 = 27 this satisfies the sum condition.

12 × 15 = 180 this satisfies the product condition.

4. Thus, we have a = 12 and b = 15.

So the quadratic factorises as (x – 12)(x – 15).