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Math Help - Easy factoring homework help

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    Easy factoring homework help

    24p^2 +4p - 4

    Can someone give me a step by step instruction on solving it?
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    Quote Originally Posted by nerdzor View Post
    24p^2 +4p - 4

    Can someone give me a step by step instruction on solving it?
    (12p-4)(2p+1)
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by nerdzor View Post
    24p^2 +4p - 4

    Can someone give me a step by step instruction on solving it?
    Do you mean factoring it?

    First factor out the common 4:
    24p^2 +4p - 4 = 4(6p^2 + p - 1)

    Now turn your attention to the trinomial:
    6p^2 + p - 1

    This is called the "ac" method.

    Multiply the leading coefficient with the constant, in this case 6 \cdot -1 = -6

    Now form a list of the pairs of factors of -6:
    1, -6
    2, -3
    3, -2
    6, -1

    Now compare the sum of each pair of factors with the coefficient of the linear term of the quadratic, in this case 1. I get that 3 + (-2) = 1. So we want to write the linear term of the quadratic as p = (1)p = (3 - 2)p = 3p - 2p.

    So
    24p^2 +4p - 4 = 4(6p^2 + p - 1)

    = 4(6p^2 + 3p - 2p - 1)

    Now factor by grouping:
    = 4([6p^2 + 3p] + [-2p - 1])

    = 4(3p~[2p + 1] + (-1)[2p + 1])

    = 4(3p - 1)(2p + 1)

    -Dan
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