📐 Synthetic Division Calculator
Enter the coefficients of a polynomial (degree up to 4) and a value c to divide the polynomial by (x – c) using synthetic division.
What is synthetic division?
Synthetic division is a shortcut method for dividing a polynomial by a linear factor of the form (x − c). It’s faster than full polynomial long division and is especially useful for testing possible roots of a polynomial.
How this calculator works
Enter the coefficients of your polynomial from the highest power down to the constant term (use 0 for any missing term), plus the value of c. The calculator brings down the leading coefficient, then repeatedly multiplies by c and adds it to the next coefficient, producing the coefficients of the quotient polynomial (one degree lower) and a final remainder.
By the Remainder Theorem, that final remainder is exactly equal to P(c) — the value of the original polynomial evaluated at x = c. If the remainder is zero, then (x − c) is a factor of the polynomial and c is a root.
This calculator is for general educational and reference purposes.