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Math Help - easy factoring problem

  1. #1
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    easy factoring problem

    I cant remember how to factor polynomials to the 3rd degree:

     x^3-2x^2+x+1

    thanks for the help
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  2. #2
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    Quote Originally Posted by discobob View Post
    I cant remember how to factor polynomials...
    To review, try here.

    The Rational Roots Test tells you to check x = -1 and x = +1, using synthetic division. Once you've found one root, you can apply the Quadratic Formula to what remains.
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  3. #3
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    so, using synthetic division, +1 is a zero. for "the rest" do you mean  -2x^2+x+1 ? If so, using the quadratic equation, zero's are -1/2 and +1. Is that correct?
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  4. #4
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    Quote Originally Posted by discobob View Post
    so, using synthetic division, +1 is a zero. for "the rest" do you mean  -2x^2+x+1 ? If so, using the quadratic equation, zero's are -1/2 and +1. Is that correct?
    Hi discobob,

    f(x)=x^3-2x^2+x+1 has no rational zeros. +1 is not a zero. Neither is -1/2.
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  5. #5
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    Quote Originally Posted by discobob View Post
    so, using synthetic division, +1 is a zero. for "the rest" do you mean  -2x^2+x+1 ? If so, using the quadratic equation, zero's are -1/2 and +1. Is that correct?
    f(1) = 1

    See attached for the graph of f(x)

    edit: if that graph looks weird that's because I zoomed in - if you sketch it it's a normal cubic
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