### Instruction: The three roots of the equation \[ax^3+bx^2+cx+d=0\]are $1,$ $2,$ and $3.$ Compute $\frac{c}{d}.$.### Response: So we know that the roots of the equation are 1, 2, and 3.
That means that $x-1$, $x-2$, and $x-3$ are factors of the polynomial.
And so the polynomial must be of the form $a(x-1)(x-2)(x-3)$.
Expanding this, we get $ax^3-6ax^2+11ax-6a$.