What is the degree of the polynomial $(3x^2 +11)^{12}$?
I also know that when I raise a binomial to a power, I can use the binomial theorem to find the terms of the expanded polynomial. In this case, $a = 3x^2$, $b = 11$, and $n = 12$. The term with the highest power of $x$ will be the one where $k = 0$, because then I have $a^{n-k} b^k = a^n = (3x^2)^{12}$. To find the degree of this term, I just need to multiply the exponent of $x^2$ by $12$, which gives me $2 \cdot 12 = 24$. Therefore, the degree of the polynomial $(3x^2 + 11)^{12}$ is 24. 