### Instruction: Find the quadratic polynomial $p(x)$ such that $p(-7) = 0,$ $p(4) = 0,$ and $p(5) = -36.$.### Response: So we know $p(-7) = 0$ and $p(4) = 0$, so we can write $p(x)$ as $a(x+7)(x-4)$.
That's correct. Now we just need to find the value of $a$.
Let's plug in $x=5$, so we get $a(5+7)(5-4) = -36$.
That simplifies to $12a = -36$, so $a = -3$.