Question

Using factor theorem, factorise the following:

\[2x^{3} + 19x^{2} + 38x + 21\]

Answer 1

Let $$f(x) = 2x^3 + 19x^2 + 38x + 21$$. 

Since $$f(-1) = -2 + 19 - 38 + 21 = 0$$, $$(x + 1)$$ is a factor. 

Dividing $$f(x)$$ by $$(x + 1)$$ gives $$2x^2 + 17x + 21$$. 

Hence, $$2x^3 + 19x^2 + 38x + 21$$

$$= (x + 1)(2x^2 + 17x + 21)$$

$$= (x + 1)(2x + 3)(x + 7)$$