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Question

Let the GCD =x+1 and LCM =x61 for gives two polynomials. Then, if f(x)=x3+1. what is g(x)?

A
(x3+1)(x1)
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B
(x31)(x+1)
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C
x
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D
x2+1+x3
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Solution

The correct option is B (x31)(x+1)

f(x)=x3+1
GCD =x+1
LCM=x61
We know that , LCM × GCD =f(x)×g(x)
g(x)=LCM×GCDf(x)=(x61)(x+1)x3+1=(x3+1)(x31)(x+1)x3+1=(x31)(x+1)
That is, g(x)=(x31)(x+1)

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