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Here is the problem: x squared plus 5x minus 36.

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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 negative 36 equals negative 36. Find two numbers whose product is negative 36 and whose sum is b equals 5: 9 and negative 4.

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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 9 and 4.

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Write the complete factorization.

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So the answer is (x minus 4)(x plus 9).

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x squared plus 5x minus 36 factors completely over the rationals as (x minus 4)(x plus 9).

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Expanding (x minus 4)(x plus 9) gives back x squared plus 5x minus 36.