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Math Help - Polynomial functions.

  1. #1
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    Polynomial functions.

    The expression 4x^3+ax^2-5x+b leaves remainders of -8 and 10 when divided by (2x-3) and (x-3) respectively. Calculate the values of a and b.
    I've attempted this question a few times by trying to use the factor theorem and then rearranging the equations and subtracting them from each other. But, I couldn't get the right answer.
    Thanks.
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  2. #2
    Super Member Quacky's Avatar
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    Windsor, South-East England
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    The Remainder Theorem

    Let F(x)=4x^3+ax^2-5x+b

    What you know so far is that F(\frac{3}{2})=-8, and that F(3)=10

    Substituting into the polynomial gives:

    1) 4(\frac{3}{2})^3+a(\frac{3}{2})^2-5(\frac{3}{2})+b=-8
    2) 4(3)^3+a(3)^2-5(3)+b=10

    Simplify, then solve for a and b. Post your working if you get stuck.
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