Question

Find the value of $$a$$ so that $$(x + 6)$$ is a factor of the polynomial $$(x^{3} + 5x^{2} - 4x + a)$$.

Answer 1

Let $$f(x) = x^{3} + 5x^{2} - 4x + a$$. 

By the Factor Theorem, $$(x + 6)$$ is a factor if $$f(-6) = 0$$.

$$f(-6) = (-6)^3 + 5(-6)^2 - 4(-6) + a$$

$$= -216 + 180 + 24 + a$$

$$= a - 12$$

Thus, $$a - 12 = 0$$, so $$a = 12$$.