SOLUTION: factor by grouping: 4x^2+28x-24x-168

Question 152135: factor by grouping:
4x^2+28x-24x-168

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!

4x^2+28x-24x-168
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First, factor out any common factor. Notice 4 is a common factor.
4(x^2+7x-6x-42)
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Notice that of there is NO common factor for the terms inside the parenthesis. The idea is to group terms together so there is a common factor.
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Grouping:
4(x^2+7x-6x-42)
4[(x^2+7x)-(6x+42)]
Notice, the sign change above -- be careful about that!
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Now, factor each "sub group":
4[(x^2+7x)-(6x+42)]
4[x(x+7)-6(x+7)]
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Between the two terms inside the [], the common factor is (x+7), factor it out:
4[x(x+7)-6(x+7)]
4[(x+7)(x-6)]
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Finally we get:
4(x+7)(x-6)

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