Factor: 6x^2 + 9x

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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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