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Here is the problem: x squared plus 5x plus 6.

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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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Use the AC method. Multiply a times c equals 1 times 6 equals 6. Find two numbers whose product is 6 and whose sum is b equals 5: 3 and 2.

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Factor by grouping. Group the first two and last two terms, factor each group, then factor out the common binomial. The roots are negative 3 and negative 2.

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Write the complete factorization.

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So the answer is (x plus 2)(x plus 3).

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x squared plus 5x plus 6 factors completely over the rationals as (x plus 2)(x plus 3).

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