Suppose that $f$ is a polynomial such that (x^2-1)*f(x)=5x^6-x^5+3x^4+x^3 - 25x^2 +38x -17. What is the degree of $f$?

The degree of the resulting product polynomial  is 6

Dividing this degree by the degree of  x^2 - 1  = 2....then f must be degree 4