Question

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

Answer 1

`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`