What is the remainder when x^2+5 is divided by x+1?

Answer: 6

The remainder theorem says that if we divide p (x) over x-k, then the remainder is r = p (k)

In this case, we have p (x) = x^2+5 and x-k = x+1 = x - (-1). So k = - 1 is plugged into p (x) to get

p (x) = x^2+5

p (-1) = (-1) ^2+5

p (-1) = 1+5

p (-1) = 6

That is why the remainder is 6. You can use polynomial long division or synthetic division to confirm this answer.