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Here is the problem: 5x squared minus 24x plus 16.

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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 5 times 16 equals 80. Find two numbers whose product is 80 and whose sum is b equals negative 24: negative 4 and negative 20.

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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 over 5 and 4.

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Write the complete factorization.

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So the answer is (5x minus 4)(x minus 4).

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5x squared minus 24x plus 16 factors completely over the rationals as (5x minus 4)(x minus 4).

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Expanding (5x minus 4)(x minus 4) gives back 5x squared minus 24x plus 16.