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Here is the problem: 2x cubed minus 18x.

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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 2x.

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

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2x cubed minus 18x factors completely over the rationals as 2x(x minus 3)(x plus 3).

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Expanding 2x(x minus 3)(x plus 3) gives back 2x cubed minus 18x.