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Here is the problem: 6x squared minus 5x minus 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 6 times negative 6 equals negative 36. Find two numbers whose product is negative 36 and whose sum is b equals negative 5: 4 and negative 9.

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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 2 over 3 and 3 over 2.

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Write the complete factorization.

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

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

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