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Math Help - Factoring Polynomials using Synthetic Division

  1. #1
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    Factoring Polynomials using Synthetic Division

    Hi,

    I am hearing synthetic division for the first time today!

    Can anyone be kind enough to explain to me what "synthetic division"? And how I can use that to solve the following:

    The question says, “use synthetic division to determine if (x + 1) is a factor of P(x) = x^4 + 3x^3 - 2x^2 -12x - 8.If so, write P(x) as (x+1) times the reduced polynomial. Then find the zeros of P(x) (with multiplicity)

    Kindly give me leads.

    Thanks
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  2. #2
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    Re: Factoring Polynomials using Synthetic Division

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  3. #3
    MHF Contributor Siron's Avatar
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    Re: Factoring Polynomials using Synthetic Division

    I think it's good you look for some examples on the internet.

    If (x+1) is a divisor of P(x) then P(x) can be factored as:
    P(x)=(x+1)\cdot(ax^3+bx^2+cx+d)

    With the method of synthetic division you'll be able to find ax^3+bx+c+d and if you apply again synthetic division you'll be able to factore: ax^3+bx+c+d=(x-a)(x^2+ax+b).

    ...
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