When p(x) = x3 + ax2 + 2x + a is divided by


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



(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:

$p(-a)=(-a)^{3}+a \times(-a)^{2}+2 \times(-a)+a$

$=-a^{3}+a^{3}-2 a+a$



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