The exponent of the numerator exceeds that of the denominator, so as x goes to infinity, the expression goes to infinity.
You can prove it by using L'Hopital's Rule should you wish.
lim x-> inf (2x^4-3x^2+2x-1) / (x^3-2x^2+2)
lim x->inf (8x^3 -6x^2+2) / (3x^2-4x)
lim x-> inf (24x^2-12x) / (6x-4)
lim x-> inf (48x-12) / 6
= infinity