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Here is the problem: x squared minus 10x plus 24.

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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 24 equals 24. Find two numbers whose product is 24 and whose sum is b equals negative 10: negative 4 and negative 6.

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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 4 and 6.

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Write the complete factorization.

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So the answer is (x minus 6)(x minus 4).

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x squared minus 10x plus 24 factors completely over the rationals as (x minus 6)(x minus 4).

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Expanding (x minus 6)(x minus 4) gives back x squared minus 10x plus 24.