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Question

Which of the following is a factor of x101 and also of x111 ?


A

x – 1

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B

x + 1

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C

x – 10

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D

x + 10

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Solution

The correct option is A

x – 1


For solving this question, we will use hit and trial method, in which we try to find the zero of polynomial by putting values like x = 1, - 1, 2 , -2 and so on.

Let p(x)=x101 and q(x)=x111

Starting with x = 1, we get

Here, p(1)=1101=11=0
Thus, (x1) is a factor of p(x)

And, q(1)=1111=11=0
Thus, (x1) is a factor of q(x)

Hence, (x1) is a factor of both x101 and x111


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