document.write( "Question 411232: I need help factoring this, i have tried and can't figure it out..\r
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Algebra.Com's Answer #289094 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

Looking at the expression $\"49x%5E2-42x%2B5\"$ , we can see that the first coefficient is $\"49\"$ , the second coefficient is $\"-42\"$ , and the last term is $\"5\"$ .

Now multiply the first coefficient $\"49\"$ by the last term $\"5\"$ to get $\"%2849%29%285%29=245\"$ .

Now the question is: what two whole numbers multiply to $\"245\"$ (the previous product) and add to the second coefficient $\"-42\"$ ?

To find these two numbers, we need to list all of the factors of $\"245\"$ (the previous product).

Factors of $\"245\"$ :

1,5,7,35,49,245

-1,-5,-7,-35,-49,-245

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

These factors pair up and multiply to $\"245\"$ .

1*245 = 245
5*49 = 245
7*35 = 245
(-1)*(-245) = 245
(-5)*(-49) = 245
(-7)*(-35) = 245

Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"-42\"$ :

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First Number	Second Number	Sum
1	245	1+245=246
5	49	5+49=54
7	35	7+35=42
-1	-245	-1+(-245)=-246
-5	-49	-5+(-49)=-54
-7	-35	-7+(-35)=-42

From the table, we can see that the two numbers $\"-7\"$ and $\"-35\"$ add to $\"-42\"$ (the middle coefficient).

So the two numbers $\"-7\"$ and $\"-35\"$ both multiply to $\"245\"$ and add to $\"-42\"$

Now replace the middle term $\"-42x\"$ with $\"-7x-35x\"$ . Remember, $\"-7\"$ and $\"-35\"$ add to $\"-42\"$ . So this shows us that $\"-7x-35x=-42x\"$ .

$\"49x%5E2%2Bhighlight%28-7x-35x%29%2B5\"$ Replace the second term $\"-42x\"$ with $\"-7x-35x\"$ .

$\"%2849x%5E2-7x%29%2B%28-35x%2B5%29\"$ Group the terms into two pairs.

$\"7x%287x-1%29%2B%28-35x%2B5%29\"$ Factor out the GCF $\"7x\"$ from the first group.

$\"7x%287x-1%29-5%287x-1%29\"$ Factor out $\"5\"$ 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.

$\"%287x-5%29%287x-1%29\"$ Combine like terms. Or factor out the common term $\"7x-1\"$

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Answer:

So $\"49%2Ax%5E2-42%2Ax%2B5\"$ factors to $\"%287x-5%29%287x-1%29\"$ .

In other words, $\"49%2Ax%5E2-42%2Ax%2B5=%287x-5%29%287x-1%29\"$ .

Note: you can check the answer by expanding $\"%287x-5%29%287x-1%29\"$ to get $\"49%2Ax%5E2-42%2Ax%2B5\"$ or by graphing the original expression and the answer (the two graphs should be identical).

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