# Synthetic Division Calculator

Synthetic division is a shortcut method for dividing polynomials by a linear factor. It is applied in cases when linear factor has the form (x-constant) with x having coefficient as 1. If x has different coefficient, it should be reduced to 1. This method involves numeric values eliminating coefficient of the polynomial equation. The difference is you subtract in long division, here you add instead. Synthetic division calculator is used to perform synthetic division of 4th-degree polynomials.

## Synthetic Division Calculation for 4th Degree Polynomials

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### Example

Consider a 4th degree polynomial equation x^{4} + 2x^{3} + 3x^{2} + 4x + 5 divided by 3x + 2.

Linear factor of the fourth degree equation is 3x + 2,

x is the difference of constant to coefficient of x with negative range.

Here, constant is 2, coefficient is 3

From 3x + 2, x = -2 / 3

Hence x = -0.6667

Using the synthetic division,

**Polynomial Result :** 1x^{3} + 1.3333x^{2} + 2.1111x + 2.5925 + **(3.2716 / 3x + 2)**