The remainder theorem tells us the value of a polynomial when `x = a` is the remainder when the polynomial is divided by `x - a`.

We'll use synthetic division to divide by `(x - 1)`:

`1`	`1`	`11`	`-22`	`17`
		`1`	`12`	`-10`
	`1`	`12`	`-10`	`7`

The last entry of the row is the remainder, `7`.

So the value of `x^3+11 x^2-22 x+17` when `x = 1` is `7`.