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Math Help - Factoring Question

  1. #1
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    Factoring Question

    How does one go about factoring Q(x) = x^3 - x^2 - x + 1. Also, My book says that since Q(1) = 0, we know that x - 1 is a factor. Why do we know this? More specifically, my two questions are (1) why does the fact that Q(1) = 0 mean that x - 1 is a factor, and (2) could you please give a step by step procedure on how to factor this equation.

    Thanks so much for your time,

    Broseidon
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  2. #2
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    Re: Factoring Question

    Quote Originally Posted by Broseidon420 View Post
    (1) why does the fact that Q(1) = 0 mean that x - 1 is a factor
    This follows from the polynomial remainder theorem (its proof is pretty simple).

    Quote Originally Posted by Broseidon420 View Post
    (2) could you please give a step by step procedure on how to factor this equation.
    You need to divide x^3 - x^2 - x + 1 by x - 1 using polynomial long division. The ratio is going to be a quadratic polynomial, and you can find its has roots (if it has them) and therefore factorize it using the quadratic formula.
    Thanks from Broseidon420
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