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# Synthetic Division Calculator

Synthetic Division Calculator is an online tool that helps to calculate the quotient and the remainder using the synthetic division method. In synthetic division, we perform the Euclidean division of polynomials by writing fewer steps and simplifying the calculations.

## What is Synthetic Division Calculator?

Synthetic Division Calculator helps you to divide a polynomial using synthetic division to find the quotient and the remainder. In synthetic division, a polynomial is divided by a linear binomial only by considering the values of the coefficients. To use the **synthetic division calculator**, enter the values in the input boxes.

### Synthetic Division Calculator

## How to Use Synthetic Division Calculator?

Please follow the steps given below to divide a polynomial by using the synthetic division calculator.

**Step 1:**Go to Cuemath's online synthetic division calculator.**Step 2**: Enter the polynomials in the given input box of the synthetic division calculator.**Step 3**: Click on the**"Divide"**button to calculate the quotient and remainder.**Step 4**: Click on**"Reset"**to clear the fields and enter new values.

## How Does Synthetic Division Calculator Work?

Using synthetic division we can divide a polynomial by a binomial of the form x - k. The formula for synthetic division is given as:

p(x)/ g(x) = Quotient + (Remainder / g(x)).

Here, p(x) is the polynomial or the dividend.

g(x) is the divisor and is a binomial of the form (x - k).

Given below are the steps to perform synthetic division:

- First, write the polynomial in the standard form from the highest degree terms to the lowest degree terms. If there are any missing terms use 0 as a coefficient.
- Set up the division by writing the coefficients of the polynomial on the right and the 'k' term of (x - k) on the left.
- Bring down the coefficient of the highest degree term.
- Now multiply this coefficient by 'k' and write the product below the second coefficient of the polynomial.
- Add the product and the second coefficient from step 4 and write the sum in the bottom row.
- Repeat this process.
- The last term obtained will be the remainder. Further, group the other coefficients to get the quotient.

## Solved Examples on Synthetic Division Calculator

**Example 1:**

Solve (2x^{2} + 3x + 1) / (x + 1) and verify it using the synthetic division calculator.

**Solution:**

**Example 2:**

Solve (x^{2} + 3) / (x - 4) and verify it using the synthetic division calculator.

**Solution:**

The quotient is x + 4 and the remainder is 19.

Similarly, you can use the synthetic division calculator to find the quotient and remainder for the following polynomials.

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

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