document.write( "Question 270244: may i have some help please?\r
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Algebra.Com's Answer #198000 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
First factor out the GCF 3 to get $\"3%28x%5E2%2B2x-8%29\"$ \r
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Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

Looking at the expression $\"x%5E2%2B2x-8\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"2\"$ , and the last term is $\"-8\"$ .

Now multiply the first coefficient $\"1\"$ by the last term $\"-8\"$ to get $\"%281%29%28-8%29=-8\"$ .

Now the question is: what two whole numbers multiply to $\"-8\"$ (the previous product) and add to the second coefficient $\"2\"$ ?

To find these two numbers, we need to list all of the factors of $\"-8\"$ (the previous product).

Factors of $\"-8\"$ :

1,2,4,8

-1,-2,-4,-8

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to $\"-8\"$ .

1*(-8) = -8
2*(-4) = -8
(-1)*(8) = -8
(-2)*(4) = -8

Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"2\"$ :

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First Number	Second Number	Sum
1	-8	1+(-8)=-7
2	-4	2+(-4)=-2
-1	8	-1+8=7
-2	4	-2+4=2

From the table, we can see that the two numbers $\"-2\"$ and $\"4\"$ add to $\"2\"$ (the middle coefficient).

So the two numbers $\"-2\"$ and $\"4\"$ both multiply to $\"-8\"$ and add to $\"2\"$

Now replace the middle term $\"2x\"$ with $\"-2x%2B4x\"$ . Remember, $\"-2\"$ and $\"4\"$ add to $\"2\"$ . So this shows us that $\"-2x%2B4x=2x\"$ .

$\"x%5E2%2Bhighlight%28-2x%2B4x%29-8\"$ Replace the second term $\"2x\"$ with $\"-2x%2B4x\"$ .

$\"%28x%5E2-2x%29%2B%284x-8%29\"$ Group the terms into two pairs.

$\"x%28x-2%29%2B%284x-8%29\"$ Factor out the GCF $\"x\"$ from the first group.

$\"x%28x-2%29%2B4%28x-2%29\"$ Factor out $\"4\"$ from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

$\"%28x%2B4%29%28x-2%29\"$ Combine like terms. Or factor out the common term $\"x-2\"$

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Answer:

So $\"x%5E2%2B2%2Ax-8\"$ factors to $\"%28x%2B4%29%28x-2%29\"$ .

In other words, $\"x%5E2%2B2%2Ax-8=%28x%2B4%29%28x-2%29\"$ .

Note: you can check the answer by expanding $\"%28x%2B4%29%28x-2%29\"$ to get $\"x%5E2%2B2%2Ax-8\"$ or by graphing the original expression and the answer (the two graphs should be identical).

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\n" ); document.write( "\n" ); document.write( "So $\"3x%5E2%2B6x-24\"$ completely factors to $\"3%28x%2B4%29%28x-2%29\"$ \n" ); document.write( "

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