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Here is the problem: x squared minus 3x minus 28.

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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 1 times negative 28 equals negative 28. Find two numbers whose product is negative 28 and whose sum is b equals negative 3: 4 and negative 7.

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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 7.

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Write the complete factorization.

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

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x squared minus 3x minus 28 factors completely over the rationals as (x minus 7)(x plus 4).

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Expanding (x minus 7)(x plus 4) gives back x squared minus 3x minus 28.