Using remainder theorem, find the reminder when $3 x^{2} + x + 7$ is divided by $x + 2$

17

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12

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9

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22

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Solution

The correct option is A $17$
Let $f (x) = 3 x^{2} + x + 7$ and
$g (x) = x + 2$
$=> x + 2 = 0$
$=> x = - 2$
The remainder when $f (x)$ is divided by $g (x)$ is $f (- 2)$ (By Remainder Theorem)
Thus, $f (- 2) = 3 (- 2)^{2} + (- 2) + 7$
$= 12 - 2 + 7$
$= 17$

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