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Math Help - factor trinomial

  1. #1
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    factor trinomial of odd exponent

    How do you factor x^3-3x^2+4 ?
    Last edited by delgeezee; December 9th 2011 at 01:52 AM.
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  2. #2
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    Re: factor trinomial of odd exponent

    Quote Originally Posted by delgeezee View Post
    How do you factor x^3-3x^2+4 ?
    x^3+x^2-4x^2+4=x^2(x+1)-4(x^2-1)......etc.
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  3. #3
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    Re: factor trinomial of odd exponent

    The "rational root theorem" says that if m/n is a rational root of ax^n+ a_{n-1}x^{n-1}+ \cdot\cdot\cdot+ a_1x+ a_0= 0, then n evenly divides the "leading coefficient", a_n, and m evenly divides the constant term, a_0. Here, the leading coefficient is 1 so n must be 1 or -1 and the constant term is 4 so m must be 1, -1, 2, -2, 4, or -4. That means any rational root must be one of 1, -1, 2, -2, 4, or -4. Try each of those until you find one that makes the polynomial 0. For that a, x- a is a factor and you can divide the polynomial by x-a to find the other factor.

    (If the polynomial does not have a rational root, it cannot be factored with integer coefficients.)
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