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Polynomial and Its General Form

When the poly...

Question

When the polynomial $a^{3} + 2 a^{2} - 5 a x - 7$ is divided by $a + 1$ , the remainder is $R_{1}$ . If $R_{1} = 14$ , find the value of $x$ .

A

1

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B

2

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C

3

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D

4

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Solution

The correct option is D $4$
When the polynomial $a^{3} + 2 a^{2} - 5 a x - 7$ is divided by $a + 1$ , the remainder is $R_{1}$ .
By the remainder theorem, the remainder is,
$R_{1} = (- 1)^{3} + 2 (- 1)^{2} - 5 (- 1) x - 7$
$14 = - 1 + 2 + 5 x - 7 = 5 x - 6$
$14 = 5 x - 6$
$14 + 6 = 5 x$
$20 = 5 x$
$∴ x = 4$

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