# Thread: Prove that a binomial is a factor

1. ## Prove that a binomial is a factor

Hi,

I hope someone can help. I'm suppose to prove that x + a is a factor of (x + a)^5 + (x - c)^5 + (a - c)^5. The textbook solution is if f(x) = (x + a)^5 + (x - c)^5 + (a - c)^5, then f(-a) = 0. I don't totally understand this solution, so could someone please elaborate on this?

Best,
Olivia

2. ## Re: Prove that a binomial is a factor

Originally Posted by otownsend
Hi,

I hope someone can help. I'm suppose to prove that x + a is a factor of (x + a)^5 + (x - c)^5 + (a - c)^5. The textbook solution is if f(x) = (x + a)^5 + (x - c)^5 + (a - c)^5, then f(-a) = 0. I don't totally understand this solution, so could someone please elaborate on this?

Best,
Olivia
what does the factor theorem say?