# SOLUTION: Hi, I am having trouble with a problem I hope some one can help me please. Factor Completety: 3x - 3x^2 + 6x - 18 I would like to thank you for your help.

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Question 139640: Hi, I am having trouble with a problem I hope some one can help me please.
Factor Completety:
3x - 3x^2 + 6x - 18
I would like to thank you for your help.

Answer by jim_thompson5910(28593)   (Show Source):
You can put this solution on YOUR website!
Are you sure it's not supposed to read: ???

Combine like terms

Factor out the GCF

Now let's focus on the inner expression

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Looking at we can see that the first term is and the last term is where the coefficients are 1 and -6 respectively.

Now multiply the first coefficient 1 and the last coefficient -6 to get -6. Now what two numbers multiply to -6 and add to the middle coefficient 1? Let's list all of the factors of -6:

Factors of -6:
1,2,3,6

-1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -6
(1)*(-6)
(2)*(-3)
(-1)*(6)
(-2)*(3)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1

First NumberSecond NumberSum
1-61+(-6)=-5
2-32+(-3)=-1
-16-1+6=5
-23-2+3=1

From this list we can see that -2 and 3 add up to 1 and multiply to -6

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

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So our expression goes from and factors further to

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