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29 August, 12:48

Which shows one way to determine the factors of x^3+5x^2-6x-30 by grouping?

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  1. 29 August, 13:16
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    The factors of this equation are x = sqrt (6), x = - sqrt (6) and x = - 5.

    In order to find these by grouping, we start by just taking the first two terms. We then pull out the greatest common factor.

    x^2 + 5x^2

    x^2 (x + 5)

    Now we do the same for the last two.

    -6x - 30

    -6 (x + 5)

    Since the two parenthesis left behind are exactly the same, we can use them along with the factors pulled out, multiplied together.

    (x^2 - 6) (x + 5)

    Now to find the factors, we simply set both parenthesis separately equal to 0.

    x + 5 = 0

    x = - 5

    x^2 - 6 = 0

    x^2 = 6

    x = + / -sqrt (6)
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