#### Question

Use the Remainder Theorem to factorise the following expression:]

`2x^3 + x^2 - 13x + 6`

#### Solution

f(x) = 2x^{3} + x^{2} – 13x + 6

Factors of constant term 6 are ±1, ±2, ±3, ±6.

By hit and trail, putting x = 2, f(2) = 2(2)^{3} + 2^{2} – 13 (2) + 6 = 0,

Hence (x – 2) is a factor of f(x) using factor theorem

So f(x)= 2x^{2} (x – 2) + 5x (x – 2) – 3 (x – 2)

= (x – 2) (2x^{2} + 5x – 3)

= (x – 2) [2x^{2} + 6x – x – 3]

= (x – 2) [2x (x + 3) – (x + 3)]

= (x – 2) (x + 3) (2x – 1)

Is there an error in this question or solution?

#### APPEARS IN

Solution Use the Remainder Theorem to Factorise the Following Expression:] `2x^3 + X^2 - 13x + 6` Concept: Remainder Theorem.