Rewrite the expression $g^4 + 12g^2 + 9$ in the form $c(g^2 + p)^2 + q$. What is $q$?
I recognize that this is a quadratic expression in terms of $g^2$, so I can try to complete the square for it. To do that, I need to factor out the coefficient of $g^4$, which is 1 in this case. So I get $g^4 + 12g^2 + 9 = (g^2 + 6)^2 - 27$. Now I can write this in the form $c(g^2 + p)^2 + q$ by letting $c = 1$, $p = 6$, and $q = -27$. Therefore, $q = -27$. 