Question

x(x+2)(x-1)(x-2)
When simplified what is the degree and classification?

Answer 1

you can see right away the deg(polynomial)=amount of x's present. thus, deg(p)=4.
you can make the polynomila shorter by combining (x-2)(x+2)=(x^2-4), which makes
p=x(x-1)(x^2-4). this is a polynomial of degree 4. not sure about what you mean by classification. If it is the amount of roots, then this polynomial has 4 roots, {0,-2,2,1}