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Here is the problem: 12x cubed minus 3x.

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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 3x.

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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 3x(2x minus 1)(2x plus 1).

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12x cubed minus 3x factors completely over the rationals as 3x(2x minus 1)(2x plus 1).

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Expanding 3x(2x minus 1)(2x plus 1) gives back 12x cubed minus 3x.