Factor $ x^3-3x^2-4x+12$

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How do I go about factoring this problem?

What is the best method? I can not factor out an $x$ since the $12$ does not have a variable. I usually use the Criss Cross method.

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2 Answers

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Using factoring by grouping:

$x^3−3x^2−4x+12=x^2(x-3)-4(x-3)=(x^2-4)(x-3)$

You can expand further by using the difference of squares $x^2-4=(x-2)(x+2)$.

The factored expression then becomes $(x-2)(x+2)(x-3)$.

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Use grouping to get $(x^2-4)(x-3)$ and then don't forget to factor $x^2-4$ as $(x+2)(x-2)$.

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