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Chapter 4: Q. 91 (page 210)

Use the Factor Theorem to prove that x-c is a factor of

xn-cn for any positive integer n.

Short Answer

Expert verified

If f(x)=xn-cnthen f(c)=0so x-cis a factor ofxn-cn

Step by step solution

01

Step 1. given data

The given expression is

xn-cn

Factor isx-c

02

Step 2. proof

Consider function f(x)=xn-cn

According to Factor Theorem, If x-cis a factor of function then f(c)=0

substitute c for x in the function

f(x)=xn-cnf(c)=cn-cnf(c)=0

the function value is zero for x=c

sox-cis a factor ofxn-cn

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