First, we try to factor x^2 + 2x + 10. That doesn't seem quite possible, so now we try to use completing the square with (x-1)^2. We get that x^2 + 2x +10 = (x-1)^2 + 4x + 9. We can still factor it more and get (x-1)*(x-1 + 4) + 13 = (x-1)*(x+3) +13. Hence, the quotient is x+3 and the remainder is 13.