Factoring - Extracting a Common Factor

Now that you have the factored form of the expression, which of the following expressions is equivalent to the expression above?

Correct. First, find the greatest common factor of $$20x$$ and 30. Both terms are divisible by 10. Write 10 down outside a pair of brackets: >$$10\cdot(\quad )$$ Populate the brackets with the remaining factors. The number 10 must be multiplied by $$\color{red}{2x}$$ to result in $$20x$$ and by $$\color{red}{3}$$ to result in 30: >$$10(\color{red}{2x}-\color{red}{3})$$

Incorrect. Indeed, 10 is the greatest common factor, but is the $$x$$ in the brackets really the remaining factor after extracting 10 from $$20x$$? Expanding $$10(x-3)$$ results in > $$10\cdot x-10\cdot 3 = 10x-30$$ This isn't equivalent to the original expression $$20x-30$$, and therefore this answer is incorrect.

Incorrect. The number 20 isn't the correct common factor, since 30 (which is one of the terms) isn't divisible by 20. Expanding $$20(2x-3)$$ results in > $$20 \cdot 2x-20 \cdot 3 = 40x-60$$ This isn't equivalent to the original expression $$20x-30$$, which proves this answer is incorrect.

Incorrect. The number 20 isn't the correct common factor, since 30 (which is one of the terms) isn't divisible by 20. Expanding $$20(x-3)$$ results in > $$20\cdot x-20 \cdot 3 = 20x-60$$ This isn't equivalent to the original expression $$20x-30$$, which proves this answer is incorrect.

The following is a basic algebra practice exercise and not a GMAT level problem: First extract the greatest common factor out of the expression below. >$$20x-30$$ Click "continue" when you're done.

$$10(2x-3)$$

$$10(x-3)$$

$$20(x-3)$$

$$20(2x-3)$$

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