Factor completely: 12x^2 − 8x.

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Multiple Choice

Factor completely: 12x^2 − 8x.

Explanation:
Look for the greatest common factor that both terms share. In 12x^2 − 8x, each term has a factor of 4x, since 12x^2 = 4x·3x and −8x = 4x·(−2). Factoring that out gives 4x(3x − 2). The inside part, 3x − 2, has no common factor and cannot be factored further over the integers, so this is the expression in completely factored form. Other written forms still hide factors inside or haven’t pulled out all common factors. For example, 2x(6x−4) can be rewritten as 4x(3x−2) if you factor further inside, and 4(3x^2−2x) or x(12x−8) likewise factor to 4x(3x−2) when you pull out the remaining common factor.

Look for the greatest common factor that both terms share. In 12x^2 − 8x, each term has a factor of 4x, since 12x^2 = 4x·3x and −8x = 4x·(−2). Factoring that out gives 4x(3x − 2). The inside part, 3x − 2, has no common factor and cannot be factored further over the integers, so this is the expression in completely factored form.

Other written forms still hide factors inside or haven’t pulled out all common factors. For example, 2x(6x−4) can be rewritten as 4x(3x−2) if you factor further inside, and 4(3x^2−2x) or x(12x−8) likewise factor to 4x(3x−2) when you pull out the remaining common factor.

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