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Math Help - Proving a factor correct

  1. #1
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    Proving a factor correct

    Hello,

    I am a grade 12 functions student with an exam tomorrow morning. I was doing one last review and a question has me stumped. I would really appreciate someone's help.

    This is what it is asking

    "Show that (x+y) is a factor of x^8-y^8"

    It seems simple, but its late here and I think I'm missing something.

    Thanks again
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by FunctionsStudent View Post
    Hello,

    I am a grade 12 functions student with an exam tomorrow morning. I was doing one last review and a question has me stumped. I would really appreciate someone's help.

    This is what it is asking

    "Show that (x+y) is a factor of x^8-y^8"

    It seems simple, but its late here and I think I'm missing something.

    Thanks again
    one way to go: keep using the difference of two squares formula:

    x^8 - y^8 = (x^4 + y^4)(x^4 - y^4) = (x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = ...

    another way, use the remainder/factor theorem: if the remainder of x^8 - y^8 \div x + y is 0, then x + y is a factor of x^8 - y^8 by the factor theorem.

    so use long division (or synthetic division) to show that the remainder is actually zero
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  3. #3
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    Ah, I was trying to use synthetic division improperly, and as soon as you mentioned remainder/factor theorem I realized that was the simplest route.

    x=(-y) therefore (-y)^8-y^8=0

    I had one of those "Ohhh..." moments.

    Your help is greatly appreciated.
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