Suppose that f(x) and g(x) are polynomials of degree 4 and 5 respectively. What is the degree of f(x^3)*g(x^2)?
We can let f(x) = x^4 and g(x) = x^5
So
f(x^3) = [ x^3 ]^4 = x^12
and
g(x^2) = [ x^2 ]^5 = x^10
f(x^3) * g (x^2) =
x^12 * x^10 =
x^22 ⇒ degree 22
