Question

Factorise the following expressions

m² + m – 72

Answer 1

m² + m – 72

This is of the form ax + bx + c

where a = 1, b = 1, c = – 72

Product = – 72	Sum = 1
1 × (– 72) = – 72	1 + (– 72) = – 71
2 × (– 36) = – 72	2 + (– 36) = – 34
3 × (– 24) = – 72	3 + (– 24) = – 21
4 × (– 18) = – 72	4 + (– 18) = – 14
6 × (– 12) = – 72	6 + (– 12) = – 6
8 × (– 9) = – 72	8 + (– 9) = – 1
9 × (– 8) = – 72	9 + (– 8) = 1

Product a × c = 1 × – 72 = – 72

Sum b = 1

The middle term m can be written as 9m – 8m

m² + m – 72 = m² + 9m – 8m – 72

= m(m + 9) – 8(m + 9)

Taking out (m + 9)

= (m + 9)(m – 8)

∴ m² + m – 72 = (m + 9)(m – 8)