Question

Using Remainder Theorem, find the remainder when $$f(x) = x^3 - 2x^2 - 5x + 6$$ is divided by $$(x + 2)$$.

Answer 1

Since the divisor is $$x + 3 = x - (-3)$$, the remainder is $$f(-3)$$.

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

$$= -8 - 8 + 10 + 6$$

$$= 0$$

Hence, the remainder is $$0$$.