Question

6x^4 + 5x^3 + 3x - 5 is divided by 3x^2 - 2x

Answer 1

for this one you have to use long division, which is a pain. better to cheat and see if you can factor and cancel

Answer 2

nope, you cannot, so you have to divide using long division
if you just need the answer, look at the part that says "quotient and remainder" here
http://www.wolframalpha.com/input/?i=%28+6x^4+%2B+5x^3+%2B+3x+-+5%29%2F%283x^2+-+2x%29