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Question

On dividing x42x29x9 by a polynomial g(x), the quotient is (x2x4) and the remainder is (3-2x). Find g(x)

A

x2+x3
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B

x2+x+3
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C

x2x+3
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D

x2+x+3
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Solution

The correct option is B
x2+x+3
f(x)=x4+2x29x9q(x)=x2x4r(x)=32x g(x)×q(x)+r(x)=f(x)g(x)×q(x)=f(x)r(x)g(x)=f(x)r(x)q(x)f(x)r(x)=(x42x29x9)(32x)x42x27x12f(x)r(x)q(x)=x42x27x12x2x4


g(x)=x2+x+3
So, correct option is b.

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