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Math Help - Factoring Polynomials Help..

  1. #1
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    Factoring Polynomials Help..

    If P(x)=3x3+x2+48x+16 contains the factor x-4i, find all the remaining factors. Write p(x) in factored form.

    So I have (x-4i) and (x+4i) as two factors which = (x2+16)

    I then divide using long polynomial division. (3x2+x+48x+16)/(x+16) = 3x+1 with no remainders.

    I find that (x-4i),(x+4i) and (3x+1) are all factors of the polynomial P(x).....Are these all the factors? Did I do this correctly?


    Thank you very much
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  2. #2
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    Re: Factoring Polynomials Help..

    Quote Originally Posted by curt26 View Post
    If P(x)=3x3+x2+48x+16 contains the factor x-4i, find all the remaining factors. Write p(x) in factored form.
    \\3x^3+x^2+48x+16\\x^2(3x+1)+16(3x+1)\\(x^2+16)(3x  +1)
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  3. #3
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    Re: Factoring Polynomials Help..

    Thank you,

    So you're saying the only factors are (x2​+16) and (3x+1)?
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    Re: Factoring Polynomials Help..

    Quote Originally Posted by curt26 View Post
    So you're saying the only factors are (x2​+16) and (3x+1)?

    Well not exactly. From that you see the roots are \pm4i~\&~\tfrac{-1}{3}.
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  5. #5
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    Re: Factoring Polynomials Help..

    Ok, so if my roots are +4i, -4i and -1/3 the factors should be (x-4i),(x+4i) and (3x+1)? Unless I'm confused somewhere..

    Thank you
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