Question

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

Answer 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.