Question

Factorise the following expressions

4x² – 8x + 3

Answer 1

4x² – 8x + 3

This is of the form ax² + bx + c with a = 4, b = – 8, c = 3

Product ac = 4 × 3 = 12

sum b = – 8

Product = 12	Sum = – 8
(–1) × (–12) = 12	(–1) + (–12) = – 13
(– 2) × (– 6) = 12	(– 2) + (– 6) = – 8

The middle term can be written as – 8x = – 2x – 6x

4x² – 8x + 3 = 4x² – 2x – 6x + 3

= 2x(2x – 1) – 3(2x – 1)

= (2x – 1)(2x – 3)

4x² – 8x + 3 = (2x – 1)(2x – 3)