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Here is the problem: 4x squared minus 12x plus 9.

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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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Recognise a special pattern. The remaining factor is a perfect square trinomial: a squared plus or minus 2ab plus b squared equals (a plus or minus b) squared.

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Write the complete factorization.

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

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4x squared minus 12x plus 9 factors completely over the rationals as (2x minus 3) squared.

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Expanding (2x minus 3) squared gives back 4x squared minus 12x plus 9.