Question

Using factor theorem, factorise the following:

\[2x^{3} + x^{2} - 13x + 6\]

Answer 1

Let $$f(x) = 2x^3 + x^2 - 13x + 6$$. 

Since $$f(2) = 16 + 4 - 26 + 6 = 0$$, $$(x - 2)$$ is a factor. 

Dividing $$f(x)$$ by $$(x - 2)$$ gives $$2x^2 + 5x - 3$$. 

Hence, $$2x^3 + x^2 - 13x + 6$$

$$= (x - 2)(2x^2 + 5x - 3)$$

$$= (x - 2)(2x - 1)(x + 3)$$