WEBVTT

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Here is the problem: x squared minus 5xy plus 6y squared.

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Factor a two-variable polynomial.

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Write the polynomial in standard form.

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Factor the homogeneous part. The remaining factor is homogeneous of degree 2, so set y equals 1, factor the one-variable polynomial x squared minus 5x plus 6, then restore y so every term has degree 2.

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Write the factorization.

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

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x squared minus 5xy plus 6y squared equals (x minus 3y)(x minus 2y).

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Expanding (x minus 3y)(x minus 2y) gives back x squared minus 5xy plus 6y squared.