Factor: 6x^2 + 9x

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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: 6x^2 + 9x

Explanation:
Factoring out the greatest common factor is the key idea. Both terms 6x^2 and 9x share an x and a factor 3, so pull out 3x to rewrite the expression as 3x(2x+3). Distributing back confirms: 3x·2x is 6x^2 and 3x·3 is 9x, so we recover the original. This is fully factored because 2x+3 cannot be broken down further over the integers. The other forms either stop short of factoring the GCF or multiply out to something different: for example, x(6x+9) only factors out an x and can be factored further to 3x(2x+3); 2x(6x+9) expands to 12x^2+18x, not 6x^2+9x; and 3x(2x-3) expands to 6x^2-9x, which doesn’t match the original.

Factoring out the greatest common factor is the key idea. Both terms 6x^2 and 9x share an x and a factor 3, so pull out 3x to rewrite the expression as 3x(2x+3). Distributing back confirms: 3x·2x is 6x^2 and 3x·3 is 9x, so we recover the original. This is fully factored because 2x+3 cannot be broken down further over the integers. The other forms either stop short of factoring the GCF or multiply out to something different: for example, x(6x+9) only factors out an x and can be factored further to 3x(2x+3); 2x(6x+9) expands to 12x^2+18x, not 6x^2+9x; and 3x(2x-3) expands to 6x^2-9x, which doesn’t match the original.

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