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Here is the problem: 9x squared minus 3x 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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Factor out the greatest common factor. Every term is divisible by 3.

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

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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 1.

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Write the complete factorization.

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So the answer is 3(x minus 1)(3x plus 2).

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9x squared minus 3x minus 6 factors completely over the rationals as 3(x minus 1)(3x plus 2).

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Expanding 3(x minus 1)(3x plus 2) gives back 9x squared minus 3x minus 6.