Question

Factorise the following:

x² – 8x + 15

Answer 1

Given: x² – 8x + 15

Step-wise calculation:

1. Identify coefficients:

a = 1

b = –8

c = 15

2. Calculate the product a × c: 

a × c = 1 × 15

a × c = 15 > 0

3. Find two numbers whose product is 15 and sum is –8: 

(–3) × (–5) = 15

(–3) + (–5) = –8

4. Split the middle term –8x into two terms using –3x and –5x: 

x² – 3x – 5x + 15

5. Factor by grouping:

x(x – 3) – 5(x – 3)

6. Take out common factor (x – 3): 

(x – 3)(x – 5)