The polynomial $P (x) = 4 x^{3} + 7 x^{2} - 5 x + t$ , when divided by $x + 1$ gives 3 as the remainder.
Find the value of ‘t’.

-3

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-4

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-5

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-6

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Solution

The correct option is C
-5

The remainder when $P (x)$ is divided by $x + 1$ is 3,
$\Rightarrow P (- 1) = 3$
$\Rightarrow 4 \times {(- 1)}^{3} + 7 \times {(- 1)}^{2} - 5 x (- 1) + t = 3$
$\Rightarrow 4 \times - 1 + 7 \times 1 + 5 + t = 3$
$\Rightarrow - 4 + 7 + 5 + t = 3$
$\Rightarrow 8 + t = 3$
$\Rightarrow t = - 5$

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