Suppose that $f(x)$ is a polynomial that has degree $6$ and $g(x)$ is a polynomial that has degree $3$. If $h(x)$ is also a polynomial such that $f(g(x)) + g(h(x)) + h(f(x))$ is a polynomial of degree $36$, then what is the degree of the polynomial $h$?

michaelcai
Sep 16, 2017

#1**+1 **

Suppose that $f(x)$ is a polynomial that has degree $6$ and $g(x)$ is a polynomial that has degree $3$. If $h(x)$ is also a polynomial such that $f(g(x)) + g(h(x)) + h(f(x))$ is a polynomial of degree $36$, then what is the degree of the polynomial $h$?

If f is of degree 6 and g is of degree 3, then the greatest degree of either f(g(x)) or g(f(x)) wil be 18

But addding these together will only result in a polynomial of degree 18 [ at most ]

So...... h ( f(x)) must itself be of degree 36 which implies that h will be of degree 6

CPhill
Sep 16, 2017