You can put this solution on YOUR website! -t^2 + 11t - 24
-1t^2 + 11t - 24
You "break" the middle term with the number and the variable into two terms.
These two terms must add to make 11x.
They also must multiply to make 24, which is the product of -1 from the t^2 and -24
These two numbers are 3 and 8 as 3+8=11 and 3*8=24.
-t^2 + 3t + 8t - 24
Factor these two parts individually:
(-t^2 + 3t) + (8t - 24)
Like this:
t*(-t + 3) + 8*(t - 3)
The brackets must be completely equal. Here you must make the first "t" which multiplies the bracket negative, and the brackets will be equal:
-t*(t - 3) + 8*(t - 3)
Now you can factor the part in the bracket and you're done.
(t-3)*(-t+8)
(