Suppose that $f$ is a polynomial such that \[(x-1)\cdot f(x)=3x^4+x^3 - 25x^2 +38x -17.\]What is the degree of $f$?
So if we multiply out $(x-1)\cdot f(x)$, we should get $3x^4+x^3-25x^2+38x-17$. That's correct.  We know that $f(x)$ is a polynomial, so let's write it as $ax^n + bx^{n-1} + \ldots + z$. So what should the leading term be? The degree of $(x-1)$ is 1, so the degree of $f(x)$ is 3. So the leading term should be $3x^3$. I see. So the leading term should be $3x^3$. That's correct.

