Question

Factorise the following expressions

c² – 4c – 12

Answer 1

This is of the form ax² + bx + c

Where a = 1, b = – 4, c = – 12, x = c

Now the product ac = 1 × – 12 = – 12 and the sum b = – 4

Product = – 72	Sum = 1
1 × (– 12) = – 12	1 + (– 12) = – 11
2 × (– 6) = – 12	2 + (– 6) = – 4

∴ The middle term – 4c can be written as 2c – 6c

∴ c² – 4c – 12 = c² + 2c – 6c – 12

= c(c + 2) – 6(c + 2)

Taking out (c + 2)

⇒ (c + 2)(c – 6)

∴ c² – 4c – 12 = (c + 2)(c – 6)