If $f(x)$ is a polynomial of degree 4, and $g(x)$ is a polynomial of degree 2, then what is the degree of polynomial $f(x) - g(x)$?
To find the degree of a polynomial, I need to look at the highest power of $x$ that appears in the polynomial. I also need to remember that when I subtract two polynomials, I subtract their corresponding coefficients. So, if $f(x) = a_4x^4 + a_3x^3 + a_2x^2 + a_1x + a_0$ and $g(x) = b_2x^2 + b_1x + b_0$, then $f(x) - g(x) = (a_4x^4 + a_3x^3 + (a_2 - b_2)x^2 + (a_1 - b_1)x + (a_0 - b_0)$. The degree of this polynomial is still 4, because the highest power of $x$ is 4 and the coefficient of $x^4$ is not zero. So, the degree of $f(x) - g(x)$ is 4. 