No, jyu is correct. However, even though we know x=0 isn't a solution, it's still more 'mathematically correct' to take out x² common, rather than divide by it.
ie.
3x^4-x³+4x²-x+3
x²(3x²-x+4-1/x+3/x²)
..
...
x²(3(x+1/x)²-(x+1/x)-2)
x²(3(x+1/x)+2)(x+1/x-1)
(3x²+2x+3)(x²-x+1)
...
...
...
x= jyu's...