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Here is the problem: 2x squared plus 7x plus 3.

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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 2 times 3 equals 6. Find two numbers whose product is 6 and whose sum is b equals 7: 6 and 1.

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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 1 over 2.

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Write the complete factorization.

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

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2x squared plus 7x plus 3 factors completely over the rationals as (2x plus 1)(x plus 3).

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Expanding (2x plus 1)(x plus 3) gives back 2x squared plus 7x plus 3.