Simplify the expression (2x^2 - 8x) / (2x).

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Prepare for the 8th Grade FAST Mathematics Test with our Pre-Algebra quiz. Study with multiple choice questions, each with hints and explanations. Build your confidence and ensure you're ready to excel!

Multiple Choice

Simplify the expression (2x^2 - 8x) / (2x).

Explanation:
Factor out the common factor in the top and cancel with the bottom. The numerator 2x^2 − 8x factors as 2x(x − 4). The denominator is 2x. Cancel the shared 2x, leaving x − 4. This works for all x except x cannot be 0, since the original expression has 2x in the denominator. So the simplified form is x − 4. For a quick check, plug in x = 2: (2·4 − 16)/(4) = (8 − 16)/4 = −8/4 = −2, and x − 4 gives 2 − 4 = −2, which matches.

Factor out the common factor in the top and cancel with the bottom. The numerator 2x^2 − 8x factors as 2x(x − 4). The denominator is 2x. Cancel the shared 2x, leaving x − 4. This works for all x except x cannot be 0, since the original expression has 2x in the denominator. So the simplified form is x − 4. For a quick check, plug in x = 2: (2·4 − 16)/(4) = (8 − 16)/4 = −8/4 = −2, and x − 4 gives 2 − 4 = −2, which matches.

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