1. the degree of f(x)=3x^2-4x^3+x^4 has degree of 2
2. the function f(x) =-2x(x-1)(x-2)(x+2) has 4 zeros, has a maximum, and has x-> -infinity, f(x)-> -infinity
This is incorrect. If the expression is $\displaystyle f\!\left(x\right)=3x^2-4x^3+x^4$, the largest power is the degree of the polynomial. What do you think is the correct answer?
2. the function f(x) =-2x(x-1)(x-2)(x+2) has 4 zeros, has a maximum, and has x-> -infinity, f(x)-> -infinity
This is correct!