document.write( "Question 262063: how would i find the answer to 8n^2+4=12n
\n" ); document.write( "? i subtracted the 12n and got 8n^2-12n+4=0
\n" ); document.write( "after that i did the gcf and got 4(2n^2-3n+1)=0 and then i got stuck \n" ); document.write( "

Algebra.Com's Answer #193078 by richwmiller(17219) $\"\"$ $\"About$

You can put this solution on YOUR website!
So far so good. You need to learn how to factor.
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Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

Looking at the expression $\"2x%5E2-3x%2B1\"$ , we can see that the first coefficient is $\"2\"$ , the second coefficient is $\"-3\"$ , and the last term is $\"1\"$ .

Now multiply the first coefficient $\"2\"$ by the last term $\"1\"$ to get $\"%282%29%281%29=2\"$ .

Now the question is: what two whole numbers multiply to $\"2\"$ (the previous product) and add to the second coefficient $\"-3\"$ ?

To find these two numbers, we need to list all of the factors of $\"2\"$ (the previous product).

Factors of $\"2\"$ :

1,2

-1,-2

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

These factors pair up and multiply to $\"2\"$ .

1*2 = 2
(-1)*(-2) = 2

Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"-3\"$ :

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First Number	Second Number	Sum
1	2	1+2=3
-1	-2	-1+(-2)=-3

From the table, we can see that the two numbers $\"-1\"$ and $\"-2\"$ add to $\"-3\"$ (the middle coefficient).

So the two numbers $\"-1\"$ and $\"-2\"$ both multiply to $\"2\"$ and add to $\"-3\"$

Now replace the middle term $\"-3x\"$ with $\"-x-2x\"$ . Remember, $\"-1\"$ and $\"-2\"$ add to $\"-3\"$ . So this shows us that $\"-x-2x=-3x\"$ .

$\"2x%5E2%2Bhighlight%28-x-2x%29%2B1\"$ Replace the second term $\"-3x\"$ with $\"-x-2x\"$ .

$\"%282x%5E2-x%29%2B%28-2x%2B1%29\"$ Group the terms into two pairs.

$\"x%282x-1%29%2B%28-2x%2B1%29\"$ Factor out the GCF $\"x\"$ from the first group.

$\"x%282x-1%29-1%282x-1%29\"$ Factor out $\"1\"$ 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.

$\"%28x-1%29%282x-1%29\"$ Combine like terms. Or factor out the common term $\"2x-1\"$

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Answer:

So $\"2%2Ax%5E2-3%2Ax%2B1\"$ factors to $\"%28x-1%29%282x-1%29\"$ .

In other words, $\"2%2Ax%5E2-3%2Ax%2B1=%28x-1%29%282x-1%29\"$ .

Note: you can check the answer by expanding $\"%28x-1%29%282x-1%29\"$ to get $\"2%2Ax%5E2-3%2Ax%2B1\"$ or by graphing the original expression and the answer (the two graphs should be identical).

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