When $p (x) = x^{3} - 3 x^{2} + 4 x + 32$ is divided by (x+2), the remainder is
(a) 0
(b) 32
(c) 36
(d) 4

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Solution

ANSWER:
(d) 4
x+2=0

⇒x=-2
By the remainder theorem, we know that when p(x) is divided by ( x + 2), the remainder is p(-2).
Now, we have:
$p (- 2) = (- 2)^{3} - 3 \times (- 2)^{2} + 4 \times - 2 + 32 = - 8 - 12 - 8 + 32 = 4$

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When $p (x) = x^{4} + 2 x^{3} - 3 x^{2} + x - 1$ is divided by (x-2), the remainder is
(a) 0
(b) -1
(c) -15
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p (x) = x^{3} - 3 x^{2} + 4 x + 50 a n d g (x) = x - 3

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