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Math Help - Solving Polynomials

  1. #1
    duckduckgoose33
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    Solving Polynomials

    The problems is:
    One factor of x^3 + 2x^2 - 23x - 60 is (x=4). Find the remianing factors.

    I tried to group them and factor but the second binomial wouldn't factor.
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  2. #2
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    Hello, duckduckgoose!

    One factor of x + 2x - 23x - 60 is: (x + 4).
    Find the remianing factors.

    Use long division: .(x + 2x - 23x - 60) (x + 4) .= .x - 2x - 15


    Therefore: .x + 2x - 23x - 60 .= .(x + 4)(x - 2x - 15) .= .(x + 4)(x + 3)(x - 5)

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  3. #3
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    Quote Originally Posted by duckduckgoose33 View Post
    The problems is:
    One factor of x^3 + 2x^2 - 23x - 60 is (x=4). Find the remianing factors.

    I tried to group them and factor but the second binomial wouldn't factor.
    They tell you x=4 is a solution,
    But that is not true!
    Perhaps you mean x=-4
    That means
    (x-(-4))=(x+4)
    Is a factor.

    Thus, use long division,
    Code:
    x^3 + 2x^2 - 23x - 60 : x + 4=x^2 - 2x-15
    x^3 +  4x^2
    -------------
    -2x^2 - 23x - 60
    -2x^2 - 8x 
    ------------
    -15x - 60
    -15x - 60
    ----------
    0
    Now we need to factor,
    x^2-2x-15
    Which factors as,
    (x-5)(x+3)
    Thus, the full factorization is,
    (x-5)(x+3)(x+4)
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