Question

Find the value of $$a$$, if $$(x - a)$$ is a factor of the polynomial $$3x^3 + x^2 - ax - 81$$.

Answer 1

Let $$f(x) = 3x^3 + x^2 - ax - 81.$$

Since $$(x - a)$$ is a factor, the Factor Theorem gives: $$f(a) = 0.$$

Substituting $$x = a$$: $$f(a) = 3a^3 + a^2 - a^2 - 81$$

$$= 3a^3 - 81$$

Therefore, $$3a^3 - 81= 0$$

$$\Rightarrow 3a^3 = 81$$

$$\Rightarrow a^3 = 27$$

Hence, $${a = 3}.$$