$f (x) = 3 x^{5} + 11 x^{4} + 90 x^{2} - 19 x + 53$ is divided by $x + 5$ , then the remainder is:

100

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- 100

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- 102

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102

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Solution

The correct option is B $- 102$
The remainder is $f (- 5)$ , so according to remainder theorem.
$∴$ $f (- 5) = 3 \times (- 5)^{5} + 11 \times (- 5)^{4} + 90 \times (- 5)^{2} - 19 \times (- 5)^{1} + 53$
$∴ f (- 5) = 9375 + 6875 + 2250 + 95 + 53$
$∴ f (- 5) = - 102$

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