Synthetic Division Calculator
Synthetic Division Lesson
What is Synthetic Division?
Synthetic division is a simplified form of polynomial division. It allows us to divide a polynomial of second or higher degree, such as x2 + 2x – 5, by a first-degree polynomial (also called a linear factor), such as x + 3.
As seen in the image above, synthetic division uses an L-shaped division line to guide us during our calculations. Once we convert our division polynomials to the correct format for synthetic division, we simply repeat multiplication and addition to find the quotient.
Compared to long division, synthetic division is more restricted in use as we must be dividing by a first-degree polynomial (also called a linear factor), but, it can often be more convenient and easier to use.
Why do we Learn About Synthetic Division?
Because synthetic division allows us to divide polynomials and therefore find the zeros (roots) of polynomials, it has countless real-world uses. Let’s check out just one of these many uses: predicting storm patterns to keep people safe from dangerous weather.
Meteorologists often use polynomials to model weather patterns. Some of these polynomials approximate when and where severe storms may occur and impact the people who live there, who need to have accurate warning far in advance to prepare for potentially dangerous weather.
A way to use these approximation polynomials for storm predictions is to solve the polynomial by finding its zeros (roots). Fortunately, synthetic division can simplify polynomials and provide us a direct path to finding these zeros (roots).
By dividing a second-degree or higher polynomial by a first-degree polynomial like we do with synthetic division, we can determine the quotient which is often another first-degree polynomial.
The quotient polynomial and polynomial we divided by (called the divisor or denominator) form a factored version of the original approximation polynomial. Because it is now factored, we can easily find the zeros (roots) of the original polynomial by setting each of the first-degree, factored polynomials equal to zero and solving for x.
Once we have found the x solutions of these factored polynomials, we now know the solutions to the polynomial for predicting the potential storms! By using synthetic division, we have potentially helped people stay out of harm’s way.
How to do a Synthetic Division Calculation (Example Problem 1)
How to do a Synthetic Division Calculation (Example Problem 2)
How the Calculator Works
The Synthetic Division Calculator on this page is written in the programming languages HTML, CSS, and JS.
HTML (HyperText Markup Language) is what creates the calculator’s framework. Every entity the builds up what we see with the calculator is coded as an HTML element. The HTML assigns identification names to each of these to help the CSS and JS access and modify them.
CSS (Cascading Style Sheets) controls how the HTML elements appear to us. It can move them around, color them, shape them, and even creates the animations of the buttons that we click. Without CSS, the calculator would not look as good or be as user-friendly!