# Synthetic Division Calculator

'Cuemath's Synthetic Division Calculator' is an online tool that helps to calculate the quotient and remainder using the synthetic method.

## What is Synthetic Division Calculator?

Cuemath's online Synthetic Division Calculator helps you to calculate the quotient and remainder using the synthetic method within a few seconds.

## How to Use Synthetic Division Calculator?

Please follow the below steps to use the synthetic division method:

**Step 1:**Enter the polynomials in the given input box**Step 2**: Click on the**"Divide"**button to calculate the quotient and remainder for given polynomials.**Step 3**: Click on**"Reset"**to clear the field and calculate the quotient and remainder for different polynomials.

## What is Synthetic Division?

When we divide a polynomial p(x) by a linear factor x−a (which is a polynomial of degree 1), Q(x) is the quotient polynomial and R(the constant term) is the remainder.

**p(x) / (x - a) = Quotient + (Remainder / (x−a)) = Q(x) + R / (x - a)**

Steps to use synthetic division method:

- Write the coefficients of the dividend and use the zero of the linear factor in the divisor's place.
- Bring the first coefficient down and multiply it with the divisor.
- Write the product below the 2nd coefficient and add the column.
- Repeat until the last coefficient. The last number is taken as the remainder.
- Take the coefficients and write the quotient.
- Note that the resultant polynomial is of one order less than the dividend polynomial.

Let's see the below example to understand briefly

**Solved Example:**

Solve (2x^{2} + 3x + 1) / (x + 1)

**Solution:**

** **

Similarly, you can try the calculator to find the quotient and remainder using the synthetic division method for

a) (x^{4} + 5x^{3} - 3x^{2 }+ 2x -8) / (x - 2)

b) (x^{3} - 5x + 2) / (x + 5)