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Math Help - Final Exam Help:/ ?

  1. #1
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    Unhappy Final Exam Help:/ ?

    So my Algebra2 Final exam is on thursday and my teacher was/is none the less incompitent . SO needless to say i'm not doing well in his class , just like every other student he teaches . So my question (out of the many of millions i have) is this:
    "GIven the polynomial and one of it's factors, find the remaining factors: 5x^3+12x^2-23x-42;(x-2)"
    if anyone could possibly help me with this i would greatly apprieciate it.
    -kaye.
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  2. #2
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    Since (x-2) is a factor of f(x) = 5x^3+12x^2-23x-42, then 5x^3+12x^2-23x-42 = (x-2)q(x), for some polynomial q(x). Divide f(x) by (x-2) to find q(x), and then factor the quadratic equation that you find. You will get  (x-2)(x-\alpha)(x-\beta) as the required factors, where \alpha and \beta are the roots of the quadratic equation q(x) = 0.
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  3. #3
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    Quote Originally Posted by mathFAIL View Post
    So my Algebra2 Final exam is on thursday and my teacher was/is none the less incompitent . SO needless to say i'm not doing well in his class , just like every other student he teaches . So my question (out of the many of millions i have) is this:
    "GIven the polynomial and one of it's factors, find the remaining factors: 5x^3+12x^2-23x-42;(x-2)"
    if anyone could possibly help me with this i would greatly apprieciate it.
    -kaye.
    synthetic division with the known zero ...

    Code:
    2] .........5..........12.........-23.........-42
    ......................10...........44..........42
    --------------------------------------------------
    ............5..........22..........21...........0
    note the last line represents the coefficients of the depressed polynomial.

    the cubic factors as

    y = (x-2)(5x^2 + 22x + 21)

    and the quadratic will also factor ...

    y = (x-2)(5x+7)(x+3)

    you should know how to find the other two zeros.
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