Show that $ (x-1) $ is a factor of $ \left(x^{10}-1\right) $ and also of $ \left(x^{11}-1\right) $.

Given:

Given expressions are $x^{10}-1$ and $x^{11}-1$.

To do :

We have to show that $x-1$ is a factor of the given expressions.

Solution :

Factor Theorem:

The factor theorem states that if $p(x)$ is a polynomial of degree $n >$ or equal to 1 and $‘a’$ is any real number, then $x-a$ is a factor of $p(x)$, if $p(a)=0$.

Let $P(x)=x^{10}-1$ and $Q(x)=x^{11}-1$.

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Updated on: 10-Oct-2022

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