Suppose that f is a polynomial and h is a polynomial of degree 5 or less such that
\((x^2+3x-3)\cdot f(x)+h(x)= -6x^6+72x^4 -50x^3 + 13x^2 +38x -44\)
What is the degree of f?
If h is degree 5 or less the terms from adding it all have exponents 5 or less
f(x) is multiplied by a polynomial of degree 2
the right side has a term of degree 6 so f(x) must be of degree 4
example x^2 * f(x)
x^2 * x^4 = x^6