PLEASE HELP ASAP Prove that x+a is a factor of (x+a)^5 + (x+c)^5 + (a-c)^5

asked Apr 17, 2019 81.9k views

5 votes

PLEASE HELP ASAP
Prove that x+a is a factor of (x+a)^5 + (x+c)^5 + (a-c)^5

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3 votes

P(x)=(x+a)^5 + (x+c)^5 + (a-c)^5

If
x+a is a factor of
P(x) , then
is a root of
P(x) .

Therefore

$(-a+a)^5+(-a+c)^5+(a-c)^5=0\\\\0^5+(-1(a-c))^5+(a-c)^5=0\\\\(-1)^5(a-c)^5+(a-c)^5=0\\\\-(a-c)^5+(a-c)^5=0\\\\0=0$

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