What must be added to $3 x^{3} + x^{2} - 22 x + 9$ so that the result is exactly divisible by $3 x^{2} + 7 x - 6$ ?

x + 3

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3 - 5 x

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2 x + 3

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3 - 7 x

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Solution

The correct option is D $2 x + 3$
Let us divide $3 x^{3} + x^{2} - 22 x + 9$ by $3 x^{2} + 7 x - 6$ by long division method as shown in the above image.

Therefore, the the remainder is $- 2 x - 3$ that is $- (2 x + 3)$

Hence, $- (2 x + 3)$ must be subtracted from $3 x^{3} + x^{2} - 22 x + 9$ that is $(2 x + 3)$ must be added to $3 x^{3} + x^{2} - 22 x + 9$ so that the resulting polynomial is exactly divisible by $3 x^{2} + 7 x - 6$ .

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