WEBVTT

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Here is the problem: x squared minus 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 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 (x minus 3)(x plus 3).

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

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