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Here is the problem: 16x squared minus 44x plus 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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Factor out the greatest common factor. Every term is divisible by 4.

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Use the AC method. Multiply a times c equals 4 times 7 equals 28. Find two numbers whose product is 28 and whose sum is b equals negative 11: negative 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 1 and 7 over 4.

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Write the complete factorization.

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So the answer is 4(4x minus 7)(x minus 1).

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16x squared minus 44x plus 28 factors completely over the rationals as 4(4x minus 7)(x minus 1).

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Expanding 4(4x minus 7)(x minus 1) gives back 16x squared minus 44x plus 28.