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Here is the problem: 16x squared plus 40x plus 21.

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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 16 times 21 equals 336. Find two numbers whose product is 336 and whose sum is b equals 40: 28 and 12.

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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 7 over 4 and negative 3 over 4.

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Write the complete factorization.

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So the answer is (4x plus 3)(4x plus 7).

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16x squared plus 40x plus 21 factors completely over the rationals as (4x plus 3)(4x plus 7).

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Expanding (4x plus 3)(4x plus 7) gives back 16x squared plus 40x plus 21.