Question

Show that (x-1) is a factor of x^n - 1

Please give correct answer !

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Answer 1

yeah sure for your help

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Thanks !

Here is your answer which you are searching for

let us proof it by induction

let n=1

$x^{0} -1$ = 1 -1 =0

let us assume that the statement is true for some value k

As it is true for k it must be true for k+1

so , our first assumption is that x -1 is a factor of $x^{k} -1$

let us divide x -1 into $x^{k+1} -1$ it end up with$x^{k-1}$

Now , divide x-1 into that ...........

Hence , (x-1) is a factor of $x^{n-1}$

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@ Brainlestuser

Answer 2

hope this helps you to write your answer.

A very happy friendship day☺️