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Synthetic Division of Polynomials

If x3+2x2+a...

Question

If $x^{3} + 2 x^{2} + a x + b$ is exactly divisible by $(x + a)$ and $(x - 1)$ , then .............

A

a = - 2

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B

b = - 1

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C

a = - 1

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D

b = - 2

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Solution

The correct options are
C $a = - 1$
D $b = - 2$
$f (1)$ and $f (- a)$ both are equal to $0$ by factor theorem.
$∴$ $f (1) = 1 + 2 + a + b = 0$ and $f (- a) = - a^{3} + 2 a^{2} - a^{2} + b = 0$
$∴$ $a + b = - 3$ $a n d$ $- a^{3} + a^{2} + b = 0$
Thus, on solving two equations we get, $a = - 1$ and $b = - 2$

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