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Chapter 4: Q. 92 (page 210)

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

role="math" localid="1646067091231" xn+cn if n鈮�1 is an odd integer

Short Answer

Expert verified

If f(x)=xn+cnand n is a positive odd integer then f(-c)=0sox+cis a factor of xn+cnwhenn is a positive odd integer

Step by step solution

01

Step 1. given data 

The given expression is

xn+cn

Factor isx+c

02

Step 2. proof 

Consider functionf(x)=xn+cn

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

substitute c for x in the function

f(x)=xn+cnf(-c)=(-c)n+cn

n is a positive odd integer

localid="1646067391807" f(-c)=-cn+cnf(-c)=0

the function value is zero for x=-c

so x+cis a factor of xn+cnwhen n鈮�1

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