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    factorising this

    $\displaystyle 6(x-3)^2+13(x-3)+5$
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  2. #2
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    Quote Originally Posted by johnsy123 View Post
    $\displaystyle 6(x-3)^2+13(x-3)+5$
    Use a dummy variable $\displaystyle X = x - 3$ so that the expression becomes

    $\displaystyle 6X^2 + 13X + 5$

    $\displaystyle = 6X^2 + 3X + 10X + 5$

    $\displaystyle = 3X(2X + 1) + 5(2X + 1)$

    $\displaystyle = (2X + 1)(3X + 5)$

    And since $\displaystyle X = x - 3$, this becomes

    $\displaystyle [2(x - 3) + 1][3(x - 3) + 5]$

    $\displaystyle = (2x - 6 + 1)(3x - 9 + 5)$

    $\displaystyle = (2x - 5)(3x - 4)$.
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