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An x-method chart shows the product AC at the top of X and B at the bottom of X. Above the chart is the expression AX² + BX + C. What is the factored form of 6x² + 13x + 6?

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Answer: (2x + 3)(3x + 2)

Explanation:

For the left value in each set of (), or the x-value, use 2 factors that multiply together to equal a, which is 6 here. Then, for the right value in each set of (), or the constant values, use 2 factors that multiply together to equal c, which is also 6 here.

There are 2 sets of factors that equal 6; 1 and 6, 2 and 3.

When we have multiple choices for factors like we do here, there is a shortcut to help determine the correct factors; try the factors that are closest to each other in value first, so we will try 2 and 3 first. Then, there's another shortcut, which is to not have values in a pair of () have a factor in common; for example, we don't want to have one of the factors be (2x + 2) because 2x and 2 are not fully factored because 2x + 2 can be factored to 2(x + 1). So, we will try 2 and 3, with a 2 and a 3 in each set of parentheses:

(2x + 3)(3x + 2)
(2x·3x) + (2x·2) + (3·3x) + (3·2)
6x² + 4x + 9x + 6
6x² + 13x + 6

So, our factored form is (2x + 3)(3x + 2).

I hope this helps! :)

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