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Here is the problem: 3x squared plus 10x minus 8.

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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 3 times negative 8 equals negative 24. Find two numbers whose product is negative 24 and whose sum is b equals 10: 12 and negative 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 4 and 2 over 3.

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Write the complete factorization.

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So the answer is (3x minus 2)(x plus 4).

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3x squared plus 10x minus 8 factors completely over the rationals as (3x minus 2)(x plus 4).

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Expanding (3x minus 2)(x plus 4) gives back 3x squared plus 10x minus 8.