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Here is the problem: x squared minus 3x minus 4.

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

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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 1 and 4.

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Write the complete factorization.

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So the answer is (x minus 4)(x plus 1).

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x squared minus 3x minus 4 factors completely over the rationals as (x minus 4)(x plus 1).

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Expanding (x minus 4)(x plus 1) gives back x squared minus 3x minus 4.