Question

Which of the following is a factor of $x^{10}-1$ and also of $x^{11}-1$ ?

• A. x – 1
• B. x + 1
• C. x – 10
• D. x + 10

Answer 1

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 $p\left(x\right)=x^{10}-1andq\left(x\right)=x^{11}-1$

Starting with x = 1, we get

Here, $p\left(1\right)=1^{10}-1=1-1=0$
Thus, $(x-1)$ is a factor of $p\left(x\right)$

And, $q\left(1\right)=1^{11}-1=1-1=0$
Thus, $(x-1)$ is a factor of $q\left(x\right)$

Hence, $(x-1)$ is a factor of both $x^{10}-1$ and $x^{11}-1$