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.

Algebra ->  Polynomials-and-rational-expressions -> 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.      Log On


   

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(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Are you sure it's not supposed to read: 3x%5E2+-+3x+%2B+6x+-+18???

3x%5E2+-+3x+%2B+6x+-+18 Start with the given expression


3x%5E2+%2B+3x+-+18 Combine like terms



3%28x%5E2%2Bx-6%29 Factor out the GCF 3


Now let's focus on the inner expression x%5E2%2Bx-6




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Looking at 1x%5E2%2B1x-6 we can see that the first term is 1x%5E2 and the last term is -6 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 1x%5E2%2B1x-6, replace 1x with -2x%2B3x (notice -2x%2B3x adds up to 1x. So it is equivalent to 1x)

1x%5E2%2Bhighlight%28-2x%2B3x%29%2B-6


Now let's factor 1x%5E2-2x%2B3x-6 by grouping:


%281x%5E2-2x%29%2B%283x-6%29 Group like terms


x%28x-2%29%2B3%28x-2%29 Factor out the GCF of x out of the first group. Factor out the GCF of 3 out of the second group


%28x%2B3%29%28x-2%29 Since we have a common term of x-2, we can combine like terms

So 1x%5E2-2x%2B3x-6 factors to %28x%2B3%29%28x-2%29


So this also means that 1x%5E2%2B1x-6 factors to %28x%2B3%29%28x-2%29 (since 1x%5E2%2B1x-6 is equivalent to 1x%5E2-2x%2B3x-6)



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So our expression goes from 3%28x%5E2%2Bx-6%29 and factors further to 3%28x%2B3%29%28x-2%29


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Answer:

So 3x%5E2+-+3x+%2B+6x+-+18 factors to 3%28x%2B3%29%28x-2%29