Question

divide 3x^4-6x^3-5x+10 by x-3

Answer 1

First: are you familiar with long division of polynomials?
Second: are you familiar with synthetic division?
Once I've heard back from you, we could move forward with one approach or the other.

Answer 2

My preliminary calculations show that x-3 does not divide into the polynomial without producing a remainder.

My suggestion here is that you choose an easier problem to practice on, before going on to do this particular problem.

Note: I interpret your 3x^4-6x^3-5x+10

to represent\[3x ^{4}-6x ^{3}+0x^2-5x +10.\] Do you also?

Answer 3

I see you're new to Open Study. Welcome!
I do hope you'll respond in some way. Please do that now, even if only to acknowledge that you've seen and read my comments.