Find the remainder when x³ + 1 divided by (x + 1)

Solution:

It is given that, polynomial x³ + 1 divided by (x + 1).

Then, f(x) = x³ + 1

The polynomial is divided by (x + 1) . Let us use the remainder theorem to find the remainder.

If f(x) is divided by (x-a) then f(a) gives the remainder.

Thus put (x + 1) = 0

x = -1, we get,

⇒ f(-1) = (-1)³ + 1

⇒ f(-1) = -1 + 1

⇒ f(-1) = 0.

So, when f(x) = x³ + 1 is divided by x + 1, the remainder obtained is zero.

Therefore, the remainder is 0.

Find the remainder when x³ + 1 divided by (x + 1)

Summary:

The remainder when x³ + 1 divided by (x + 1) is 0.