2 years ago

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

Mathematics

1 answer:

Brums [2.3K]2 years ago

6 0

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

If $x+a$ is a factor of $P(x)$ , then $-a$ 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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