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Here is the problem: 3x squared minus 12.

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Factor a polynomial over the rational numbers.

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Write the polynomial in standard form.

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Factor out the greatest common factor. Every term is divisible by 3.

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Recognise a special pattern. The remaining factor is a difference of squares: a squared minus b squared equals (a minus b)(a plus b).

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Write the complete factorization.

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So the answer is 3(x minus 2)(x plus 2).

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3x squared minus 12 factors completely over the rationals as 3(x minus 2)(x plus 2).

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Expanding 3(x minus 2)(x plus 2) gives back 3x squared minus 12.