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

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