A polynomial is an algebraic expression having multiple terms. For example, the expression is a polynomial having 3 terms. It is also known as trinomial because it has 3 terms. Similarly, is a binomial expression because it has 2 terms. Binomials and trinomials are polynomial functions because they contain more than one term unlike monomials. A monomial is not a polynomial because it does not satisfy the basic definition of a polynomial.

Adding and subtracting polynomials is easy because we just combine the like terms and apply the arithmetic operations of addition and subtraction. On the other hand, the division of polynomial can be tricky. We can divide two polynomials expressions either by using long division or by using synthetic division. In algebra, a long division method is used for dividing one polynomial by another. The polynomial which is a divisor in long division is either of the same degree or of the lower degree than the polynomial in the dividend.

Polynomial long division method can be done manually following step by step instructions and rules. The length of the division depends upon the degree of a polynomial.

The expression used to depict the outcome of the polynomial division is given below:

A = BQ + R

Here, A is the dividend, B is the divisor, Q and R are quotient and remainder respectively.

A polynomial yields a zero remainder if the divisor B is the factor of the dividend A. Before solving polynomial division problems, we need to arrange the polynomial function in the dividend in the descending order. In this article, we will discuss how to divide polynomials using the long division method through different examples. So, let us get started.

## Example 1

Divide by .

### Solution

In the above division problem, is the dividend and is the divisor. The highest degree of the polynomial is 5. We repeat the process in step 1 again and again until we reach the remainder.

Follow these step by step instructions to divide the polynomials and find the quotient.

**Step 1**

- Write the polynomial in the form
- We will start by dividing the first term of the dividend by the first term of the divisor. . Write this answer above at the quotient's place. It is the first term of the quotient.
- Now, we need to multiply with the divisor . .
- Subtract it from the dividend . This is the remaining part of the dividend.

**Step 2**

- Divide the first term of the remaining dividend in the step 1 by the first term of the divisor. . Write this result in the quotient's place. This is the second term of the quotient.
- Now, multiplying by will give us the following result.

- Subtract it from the remaining dividend. . This is the remaining part of the dividend.

**Step 3**

- Divide the leading term of the remaining part of the dividend from step 2 by the first term of the divisor. . Write it at the quotient's place. This is the third term of the quotient.
- Multiply by the divisor to get .
- Subtract it from the remaining dividend . This is the remaining part of the dividend.

**Step 4**

- Divide the first term of the remaining dividend in step 3 by the first term of the divisor. . Write it at the quotient's place. This is the fourth term of the quotient.
- Multiply it with the divisor to obtain .
- Subtract it from the remaining dividend to get . This is the remaining part of the dividend.

**Step 5**

- Divide the first term of the divisor by the first term of the remaining dividend. . Write this result at the quotient's place. This is the fifth term of the quotient.
- Multiply the divisor by 1 to get .
- Subtract from the remaining dividend to get 0.
- Hence, your division is complete.

Remember that when a polynomial is completely divisible by another polynomial, then it means that the divisor is the factor of the dividend. In the above example, is the factor of the polynomial .

## Leave a Reply