Question

Using factor theorem, factorise the following:

\[6x^{3} - 7x^{2} - 11x + 12\]

Answer 1

Let $$f(x) = 6x^3 - 7x^2 - 11x + 12$$. 

Since $$f(1) = 6 - 7 - 11 + 12 = 0$$, $$(x - 1)$$ is a factor. 

Dividing $$f(x)$$ by $$(x - 1)$$ gives $$6x^2 - x - 12$$. 

Hence, $$6x^3 - 7x^2 - 11x + 12$$

$$= (x - 1)(6x^2 - x - 12)$$

$$= (x - 1)(2x - 3)(3x + 4)$$