Question

Factor Completely:

3t^3 + 5t^2 - 12t

first take out the t

so you have:
t(3t^2 + 5t - 12)
you should be able to factor it easily from there-- what numbers multiply to get (12 x 3) 36 and add to get 5?
4 and 9.
so, you will take 9 and 4 and replace it with the 5, for -9t + 4t = =5t.
so, you have:

t(3t^2 + 5t - 12)
t(3t^2 - 9t + 4t - 12)
t(3t(t - 3) 4(t - 3)) =
t(3t + 4)(t - 3)