Question

Using factor theorem, factorise the following:

\[2x^{3} + 3x^{2} - 9x - 10\]

Answer 1

Let $$f(x) = 2x^3 + 3x^2 - 9x - 10$$. 

Since $$f(2) = 16 + 12 - 18 - 10 = 0$$, $$(x - 2)$$ is a factor. 

Dividing $$f(x)$$ by $$(x - 2)$$ gives $$2x^2 + 7x + 5$$. 

Hence, $$2x^3 + 3x^2 - 9x - 10$$

$$= (x - 2)(2x^2 + 7x + 5)$$

$$= (x - 2)(2x + 5)(x + 1)$$