The expression $x^2 - 16x + 60$ can be written in the form $(x - a)(x - b)$, where $a$ and $b$ are both nonnegative integers and $a > b$. What is the value of $3b - a$?
We start off by factoring this quadratic. Wait, I thought you said we were going to use the quadratic formula. Ok, so the quadratic formula is: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$. That's correct. Now, let's plug in the values from our equation into the quadratic formula. Our equation is $x^2 - 16x + 60$. Right. So that means that $a = 1$, $b = -16$, and $c = 60$. That's correct. Now let's write our factored quadratic as $(x-a)(x-b)$. Looking at this, we can see that $a=10$ and $b=6$. Therefore, we get $3b-a=3(6)-10=8$. So $3b-a=8$.

