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

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Study for the 8th Grade FAST Mathematics Pre-Algebra Test. Enhance your skills with interactive flashcards and multiple choice questions, each containing hints and explanations to boost your comprehension and readiness for the exam. Get ready to ace your test!

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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