What is the remainder when x^3 + 2 is divided by x + 1?

To find the remainder when dividing the polynomial x³ + 2 by x + 1, we can use the Remainder Theorem. The Remainder Theorem states that the remainder of the polynomial f(x) when divided by x – c is equal to f(c).

In our case, we want to divide by x + 1, which can be rewritten as x – (-1). Therefore, we need to evaluate the polynomial f(x) = x³ + 2 at x = -1.

Now, let’s substitute -1 into the polynomial:

f(-1) = (-1)³ + 2

= -1 + 2

= 1

So, the remainder when x³ + 2 is divided by x + 1 is 1.