Synthetic Division Calculator

What is Synthetic Division?

Synthetic division is a simplified method of dividing polynomials. It is an efficient alternative to long division and is particularly useful when dividing a polynomial by a linear factor. The method is most commonly used in algebra, particularly for dividing polynomials of higher degrees.

This method is faster because it eliminates the need for writing out all the terms in the long division process. Instead, synthetic division uses coefficients to streamline the division process.

How to Use the Synthetic Division Calculator

Our synthetic division calculator makes the process even easier. Follow these simple steps to use it:

1. Input the coefficients of the dividend polynomial.
2. Enter the root of the divisor (the value that sets the linear factor to zero).
3. Click on "Calculate" to get the quotient and remainder.
4. The results will be displayed, showing both the quotient and the remainder of the division.

Advantages of Synthetic Division

Here are some of the main advantages of using synthetic division:

• Faster: Synthetic division is faster than long division, especially when dealing with high-degree polynomials.
• Simpler: The process eliminates unnecessary steps, making it easier to handle.
• Efficient: It provides the quotient and remainder with fewer calculations, saving time.

Example of Synthetic Division

Let's divide the polynomial 2x^3 + 3x^2 - 4x - 5 by the binomial x - 1 using synthetic division:

            1 |  2   3   -4   -5
              |      2   5    1
            -----------------------
                2   5    1   -4
        

The quotient is 2x^2 + 5x + 1 with a remainder of -4.

When to Use Synthetic Division

Synthetic division is ideal when:

• You are dividing a polynomial by a linear divisor.
• You need to quickly find the quotient and remainder for polynomial division.
• You want to save time on algebraic calculations.