synthetic division

A shortcut for long division by $x - c$ , using only the coefficients.

Synthetic division divides a polynomial by a linear divisor $x - c$ using only its coefficients, skipping the variables entirely: bring down the leading coefficient, then repeatedly multiply by $c$ and add. The bottom row gives the quotient's coefficients and, last, the remainder.

Examples

Dividing $x^3 - 2x^2 - 5x + 6$ by $x - 3$ synthetically gives the same quotient and remainder as long division, in far fewer steps.