When $p (x) = x^{3} + a x^{2} + 2 x + a$ is divided by (x+a), the remainder is:
(a) 0
(b) a
(c) -a
(d) 2a

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Solution

x+a=0⇒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

ANSWER: (c) − a

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