Question

Using factor theorem, factorise the following:

\[3x^{3} + 2x^{2} - 19x + 6\]

Answer 1

Let $$f(x) = 3x^3 + 2x^2 - 19x + 6$$. 

Since $$f(2) = 24 + 8 - 38 + 6 = 0$$, $$(x - 2)$$ is a factor. 

Dividing $$f(x)$$ by $$(x - 2)$$ gives $$3x^2 + 8x - 3$$. 

Hence, $$3x^3 + 2x^2 - 19x + 6$$

$$= (x - 2)(3x^2 + 8x - 3)$$

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