Factor: 8x^2 + 12x

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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

Factor: 8x^2 + 12x

Explanation:
Factoring out the greatest common factor. In 8x^2 + 12x, both terms share 4x, since 8x^2 = 4x·2x and 12x = 4x·3. Pulling out 4x leaves 2x + 3, so it factors as 4x(2x+3). Checking by distributing confirms: 4x·2x = 8x^2 and 4x·3 = 12x, which matches the original expression. Other forms don’t fit because they change the middle term when expanded (for example, 2x(4x+9) expands to 8x^2 + 18x) or leave the expression unfactored. So the correct factorization is 4x(2x+3).

Factoring out the greatest common factor. In 8x^2 + 12x, both terms share 4x, since 8x^2 = 4x·2x and 12x = 4x·3. Pulling out 4x leaves 2x + 3, so it factors as 4x(2x+3). Checking by distributing confirms: 4x·2x = 8x^2 and 4x·3 = 12x, which matches the original expression. Other forms don’t fit because they change the middle term when expanded (for example, 2x(4x+9) expands to 8x^2 + 18x) or leave the expression unfactored. So the correct factorization is 4x(2x+3).

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