Question:
When $p(x)=x^{3}+a x^{2}+2 x+a$ is divided by $(x+a)$, the remainder is
(a) 0
(b) $-1$
(c) $-15$
(d) 21
Solution:
(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:
$p(-a)=(-a)^{3}+a \times(-a)^{2}+2 \times(-a)+a$
$=-a^{3}+a^{3}-2 a+a$
$=-a$