8t^3-22t^2-5t+12 divided by 4t+3

I'm assuming polynomial long division.

2t^{2 }- 7t + 4

4t+3 | 8t^{3 }- 22t^{2 }- 5t + 12

8t^{3 }+ 6t^{2} = 2t^{2}(4t+3)

-28t^{2} - 5t

-28t^{2 }- 21t = -7t(4t+3)

16t + 12

16t + 12 = 4(4t+3)

0

Thus (8t^{3} - 22t^{2} - 5t + 12) / (4t + 3) = 2t^{2} - 7t + 4