Question

Ste2p by step dividing polynomials
4x^4+8x^3+x-3 divided by 2x

Answer 1

You can do this using long division:

__________________________________
2x | 4x^4 + 8x^3 + x - 3

========================

_2x^3____________________________
2x | 4x^4 + 8x^3 + x - 3
4x^4
-----
0 + 8x^3 + x - 3

========================

_2x^3 + 4x^2 ____________________
2x | 4x^4 + 8x^3 + x - 3
4x^4
-----
0 + 8x^3 + x - 3
8x^3
-----
0 + x - 3

========================

_2x^3 + 4x^2 + 1/2 ____________
2x | 4x^4 + 8x^3 + x - 3
4x^4
-----
0 + 8x^3 + x - 3
8x^3
-----
0 + x - 3
x
--
0 - 3

So the result is 2x^3 + 4x^2 + 1/2 with a remainder of -3. Did you follow how that is done?