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Math Help - polynomial division + simultaneous equations + other :S

  1. #1
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    polynomial division + simultaneous equations + other :S

    Sorry about ridiculous title, but i wasnt sure ....

    1) it is given that f(x)= xcubed+3xsquared-6x-8 (having large problems with the maths layout thing)

    hence express f(x) as a product of 3 linear factors

    2)Solve 4a+2b+12=0    and     a-b+3=0

    The 0's are really throwing me on this one :S
    Last edited by vanpopta; October 2nd 2008 at 01:54 PM. Reason: maths box is being awkward :S
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  2. #2
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    1. f(x) = x^3 + 3x^2 - 6x - 8

    Try factoring out x - 2.

    x^2(x - 2) = x^3 - 2x^2

    x^3 + 3x^2 - 6x - 8
    -(x^3 - 2x^2)
    = 5x^2 - 6x - 8

    5x(x - 2) = 5x^2 - 10x

    5x^2 - 6x - 8
    -(5x^2 - 10x)
    = 4x - 8

    4(x - 2) = 4x - 8

    4x - 8
    -(4x - 8)
    = 0

    \frac{x^3 + 3x^2 - 6x - 8}{x - 2} = x^2 + 5x + 4

    x^3 + 3x^2 - 6x - 8 = (x - 2)(x^2 + 5x + 4) = (x - 2)(x + 1)(x + 4)

    2. Change the system to
    4a + 2b = -12
     a - b = -3.

    Multiplying the second equation by 2 yields
    4a + 2b = -12
    2a - 2b = -6

    Adding those two equations yields
    6a = -18.

    Can you finish?
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  3. #3
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    1st one = wow! so complicated

    2nd one = i feel stupid :P


    Thanks so much
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  4. #4
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    The process I used for solving the first problem is known as long division of polynomials (and a little bit of factoring). For polynomials of degree 3 or greater, you will have to try dividing the polynomial by different factors using either this method or synthetic division, which is basically a symbolic representation of long division.
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