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Factoring Help, Finding two variables

  1. Sep 15, 2014 #1
    1. The problem statement, all variables and given/known data

    If f(x) = mx^3 + gx^2 - x + 3 is divided by x - 1, the remainder is 3. If f(x) is divided by x + 3, the remainder is -1. What are the values of m and g?

    2. Relevant equations

    Remainder Theorum/Factor Theorum

    3. The attempt at a solution

    Here is what I did:

    f(x)=mx^3+gx^2-x+3

    x -1 remainder = 3

    3=m(1)^3+g(1)^2-(1)+3
    3=m+g-1+3
    1=m+g

    x + 3, remainder = -1

    -7=m(-3)^3+g(-3)^2-(-3)+3
    -7=-27m+9g+3+3
    -----------------------

    Past that point is where I start getting fractions to my answers which don't lead me anywhere close to my answer. Where did I make a mistake and how can I solve it?
     
  2. jcsd
  3. Sep 15, 2014 #2

    LCKurtz

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    Shouldn't those -7's be -1's? And I think the (small) fractions you get will work.
     
  4. Sep 16, 2014 #3
    Yeah, I messed up the equation:

    -1=m(-3)^3+g(-3)^2-(-3)+3
    -1=-27m+9g+3+3

    collect like terms:

    -7=-27m+9g

    -1=(-27/7)n - (-9/7)g

    As you can see I end up with some strange numbers. I never got the correct answer with them so I assume they're wrong. And yet, there's no possible way I can get a -9 or even a -3 to factor those numbers.
     
    Last edited: Sep 16, 2014
  5. Sep 16, 2014 #4

    LCKurtz

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    You have ##m+g=1## and ##-27m+9g = -7##. Two equations and two unknowns. Just solve them.
     
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