document.write( "Question 295320: I am in algebra 2 this year. also i am really bad at any math. i need help on how to factor and foil x2 - 6x + 9. i dont undrestand any of this. it looks like it is in another language.\r
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Algebra.Com's Answer #212827 by jim_thompson5910(35256) $\"\"$ $\"About$

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 $\"x%5E2-6x%2B9\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"-6\"$ , and the last term is $\"9\"$ .

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

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 $\"-3x-3x\"$ . Remember, $\"-3\"$ and $\"-3\"$ add to $\"-6\"$ . So this shows us that $\"-3x-3x=-6x\"$ .

$\"x%5E2%2Bhighlight%28-3x-3x%29%2B9\"$ Replace the second term $\"-6x\"$ with $\"-3x-3x\"$ .

$\"%28x%5E2-3x%29%2B%28-3x%2B9%29\"$ Group the terms into two pairs.

$\"x%28x-3%29%2B%28-3x%2B9%29\"$ Factor out the GCF $\"x\"$ from the first group.

$\"x%28x-3%29-3%28x-3%29\"$ Factor out $\"3\"$ 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.

$\"%28x-3%29%28x-3%29\"$ Combine like terms. Or factor out the common term $\"x-3\"$

$\"%28x-3%29%5E2\"$ Condense the terms.

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Answer:

So $\"x%5E2-6%2Ax%2B9\"$ factors to $\"%28x-3%29%5E2\"$ .

In other words, $\"x%5E2-6%2Ax%2B9=%28x-3%29%5E2\"$ .

Note: you can check the answer by expanding $\"%28x-3%29%5E2\"$ to get $\"x%5E2-6%2Ax%2B9\"$ or by graphing the original expression and the answer (the two graphs should be identical).

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