### Instruction: What is the remainder when $2x^2-17x+47$ is divided by $x-5$?### Response: So we want to divide $2x^2 - 17x + 47$ by $x-5$.
Right. So we need to ask ourselves, "How many times does $x$ go into $2x^2$?".
Well, $x$ goes into $2x^2$ $2x$ times.
That's right. So we need to multiply $2x$ by $x-5$.
That gives us $2x^2 - 10x$.
Now we need to subtract that from the original polynomial.
So we get $2x^2 - 17x + 47 - (2x^2 - 10x) = 7x + 47$.
Now we need to ask ourselves, "How many times does $x$ go into $7x$?".
Well, $x$ goes into $7x$ $7$ times.
That's right. So we need to multiply $7$ by $x-5$.
That gives us $7x - 35$.
Now we need to subtract that from the polynomial we got after the first subtraction.
So we get $7x + 47 - (7x - 35) = 82$.