Synthetic Division Calculator

Divide a polynomial p(x) by the linear factor (x − r) using synthetic division. Returns the quotient coefficients and the remainder (which also equals p(r) by the remainder theorem).

Frequently Asked Questions

When can I use synthetic division?

Only when dividing by a linear factor of the form (x minus r). For higher-degree divisors, use polynomial long division.

What is the remainder theorem?

Dividing p(x) by (x minus r) gives a remainder equal to p(r). Synthetic division therefore is also the fastest way to evaluate a polynomial at a point.

How is it used in finding roots?

If a rational root candidate gives remainder zero, it is a root. Synthetic division then yields a depressed polynomial of degree one lower, which you keep factoring.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.