SOLUTION: factor completely -3t^3+3t^2-6t

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Question 119703: factor completely -3t^3+3t^2-6t
Found 2 solutions by scott8148, jim_thompson5910:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
first, factors common to all terms __ -3t(t^2-t+2)

the remaining trinomial is not factorable

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-3t%5E3%2B3t%5E2-6t Start with the given expression


-3t%28t%5E2-t%2B2%29 Factor out the GCF -3t


Now let's focus on the inner expression t%5E2-t%2B2




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Looking at t%5E2-t%2B2 we can see that the first term is t%5E2 and the last term is 2 where the coefficients are 1 and 2 respectively.

Now multiply the first coefficient 1 and the last coefficient 2 to get 2. Now what two numbers multiply to 2 and add to the middle coefficient -1? Let's list all of the factors of 2:



Factors of 2:
1,2

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

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

note: remember two negative numbers multiplied together make a positive 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
121+2=3
-1-2-1+(-2)=-3

None of these pairs of factors add to -1. So the expression t%5E2-t%2B2 cannot be factored

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Answer:
So -3t%5E3%2B3t%5E2-6t factors to -3t%28t%5E2-t%2B2%29