WEBVTT

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Here is the problem: 25x squared minus 20x plus 4.

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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 (5x minus 2) squared.

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25x squared minus 20x plus 4 factors completely over the rationals as (5x minus 2) squared.

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Expanding (5x minus 2) squared gives back 25x squared minus 20x plus 4.