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 $$f(3) = 54 - 9 - 39 - 6 = 0$$, $$(x - 3)$$ is a factor. 

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

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

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

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