document.write( "Question 255113: Please factor is possible; otherwise, write \"not factorable\".\r
\n" ); document.write( "\n" ); document.write( "9X squared plus 6X plus 1.\r
\n" ); document.write( "\n" ); document.write( "Sorry I did not know how to insert the squared sign. \n" ); document.write( "

Algebra.Com's Answer #187417 by richwmiller(17219) $\"\"$ $\"About$

You can put this solution on YOUR website!
9x^2+6x+1
\n" ); document.write( "(3x+1)^2
\n" ); document.write( "square sign is ^2 using ^ above the 6
\n" ); document.write( "Do you also not know the plus sign since you wrote out plus?\r
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Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

Looking at the expression $\"9x%5E2%2B6x%2B1\"$ , we can see that the first coefficient is $\"9\"$ , the second coefficient is $\"6\"$ , and the last term is $\"1\"$ .

Now multiply the first coefficient $\"9\"$ by the last term $\"1\"$ to get $\"%289%29%281%29=9\"$ .

Now the question is: what two whole numbers multiply to $\"9\"$ (the previous product) and add to the second coefficient $\"6\"$ ?

To find these two numbers, we need to list all of the factors of $\"9\"$ (the previous product).

Factors of $\"9\"$ :

1,3,9

-1,-3,-9

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

These factors pair up and multiply to $\"9\"$ .

1*9 = 9
3*3 = 9
(-1)*(-9) = 9
(-3)*(-3) = 9

Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"6\"$ :

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First Number	Second Number	Sum
1	9	1+9=10
3	3	3+3=6
-1	-9	-1+(-9)=-10
-3	-3	-3+(-3)=-6

From the table, we can see that the two numbers $\"3\"$ and $\"3\"$ add to $\"6\"$ (the middle coefficient).

So the two numbers $\"3\"$ and $\"3\"$ both multiply to $\"9\"$ and add to $\"6\"$

Now replace the middle term $\"6x\"$ with $\"3x%2B3x\"$ . Remember, $\"3\"$ and $\"3\"$ add to $\"6\"$ . So this shows us that $\"3x%2B3x=6x\"$ .

$\"9x%5E2%2Bhighlight%283x%2B3x%29%2B1\"$ Replace the second term $\"6x\"$ with $\"3x%2B3x\"$ .

$\"%289x%5E2%2B3x%29%2B%283x%2B1%29\"$ Group the terms into two pairs.

$\"3x%283x%2B1%29%2B%283x%2B1%29\"$ Factor out the GCF $\"3x\"$ from the first group.

$\"3x%283x%2B1%29%2B1%283x%2B1%29\"$ 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.

$\"%283x%2B1%29%283x%2B1%29\"$ Combine like terms. Or factor out the common term $\"3x%2B1\"$

$\"%283x%2B1%29%5E2\"$ Condense the terms.

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Answer:

So $\"9%2Ax%5E2%2B6%2Ax%2B1\"$ factors to $\"%283x%2B1%29%5E2\"$ .

In other words, $\"9%2Ax%5E2%2B6%2Ax%2B1=%283x%2B1%29%5E2\"$ .

Note: you can check the answer by expanding $\"%283x%2B1%29%5E2\"$ to get $\"9%2Ax%5E2%2B6%2Ax%2B1\"$ or by graphing the original expression and the answer (the two graphs should be identical).

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