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

Question.

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


Solution:

Let $f(p)=p^{10}-1$ and $g(p)=p^{11}-1$

Putting $p=1$ in $f(p)$, we get

$f(1)=1^{10}-1=1-1=0$

Therefore, by factor theorem, $(p-1)$ is a factor of $\left(p^{10}-1\right)$.

Now, putting $p=1$ in $g(p)$, we get

$g(1)=1^{11}-1=1-1=0$

Therefore, by factor theorem, $(p-1)$ is a factor of $\left(p^{11}-1\right)$.

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now