Question

By factor theorem, show that (x + 3) and (2x – 1) are factors of 2x² + 5x – 3.

Answer 1

Let x + 3 = 0 then x = – 3

Substituting the value of x in f(x)

f(x) = 2x² + 5x – 3

= 2(–3)² + 5(–3) –3

f(–3) = 18 – 15 – 3 = 0

∵ Remainder = 0,

then x + 3 is a factor

Again let 2x - 1 = 0,

then x = `(1)/(2)`

Substituting the value of x in f(x),

f(x) = 2x² + 5x – 3

`f(1/2) = 2(1/2)^2 + 5(1/2) -3`

= `2 xx (1)/(4) + (5)/(2) - 3`

= `(1)/(2) + (5)/(2) - 3` = 0

∵ Remainder = 0,

∴ 2x – 1 is also a factor

Hence, proved.