Question

When p(x) = x³ + ax² + 2x + a is divided by (x + a), the remainder is
(a) 0
(b) −1
(c) −15
(d) 21

Answer 1

(c) −a

$x+a=0\Rightarrow x=-a$
By the remainder theorem, we know that when p (x) is divided by (x + a), the remainder is p (−a).
Thus, we have:
$$\begin{gathered} p\left(-a\right)={\left(-a\right)}^3+a\times {\left(-a\right)}^2+2\times \left(-a\right)+a \\ =-a^3+a^3-2a+a \\ =-a \end{gathered}$$