Question 119703


{{{-3t^3+3t^2-6t}}} Start with the given expression



{{{-3t(t^2-t+2)}}} Factor out the GCF {{{-3t}}}



Now let's focus on the inner expression {{{t^2-t+2}}}





------------------------------------------------------------




Looking at {{{t^2-t+2}}} we can see that the first term is {{{t^2}}} 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


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">2</td><td>1+2=3</td></tr><tr><td align="center">-1</td><td align="center">-2</td><td>-1+(-2)=-3</td></tr></table>

None of these pairs of factors add to -1. So the expression {{{t^2-t+2}}} cannot be factored


------------------------------------------------------------






Answer:

So {{{-3t^3+3t^2-6t}}} factors to {{{-3t(t^2-t+2)}}}