Let's suppose that we have polynomial of degree greater than equal to 1 and is a polynomial of degree equal to 1.

Remainder theorem states that when is divided by then remainder is equal to . Let's cover some examples.

**Find the remainder when is divided by .**

Here, we have and .

Therefore, remainder =

**Is divisible by ?**

or

**Is 2 zero of the polynomial ?**

We can again use remainder theorem to check this. Here, we have and .

Therefore, remainder = .

Remainder equal to 0 means that is divisible by . It also means that 2 is the zero of polynomial .

**Is divisible by .**

Or

**Is -2 zero of the polynomial ?**

In this problem, we have and .

because . Read remainder theorem carefully.

Therefore, remainder

Remainder is equal to 0 which means that is divisible by . It also means that -2 is the zero of polynomial .

**GMAT Sample Problem:**

What is the remainder when is divided by ?

(A) 1

(B) 77

(C) 2

(D) -1

(E) None of these

Again using the remainder theorem, we can find the remainder when is divided by .

Here, we have . Therefore, remainder = .

Therefore, the answer is **(D)**.