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Thread: Prove that a binomial is a factor

  1. #1
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    Question 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
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    Re: Prove that a binomial is a factor

    Quote Originally Posted by otownsend View Post
    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?
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