1. [tex]2x^3 - \frac{1}{x} =2x^3 - x^{-1}[/tex] is not a polynomial, because the degree of second term is negative (-1);
2. [tex]x^3y - 3x^2 + 6x [/tex] is a polynomial of 4th degree (the highest degree of all terms is 3+1=4);
3. [tex]y^2 + 5y - \sqrt{3} [/tex] is a polynomial of 2th degree (the highest degree of all terms is 2);
4. [tex]2- \sqrt{4x} =2-1x^{ \frac{1}{2} }[/tex] is not a polynomial, because the degree of second term is a fraction [tex]\frac{1}{2}[/tex];
5. [tex]-x \sqrt{6} [/tex] is a monomial with 1st degree;
6. [tex]-(1/3)^{x^3} - (1/2)^{x^2}+ 1/4[/tex] is not a polynomial, because here the variable x is placed in degree.
