Synthetic Division

Pre-Calculus · Axiom Academy

Dividing a polynomial by (x - c) with nothing but its coefficients — bring down, multiply, add, march across. Synthetic division only works for a divisor of the form x - c . Pull the coefficients of the dividend into a row, and put the divisor's c in a box on the left. For x - 2 we use c = 2 ; for x + 2 = x - (-2) we would use c = -2 . The coefficients become the top row The divisor's root c goes in the box The first move is always the same: take the leading coefficient and drop it straight down into the bottom result row , untouched. That number is the first coefficient of your quotient. The leader falls straight through 3. Multiply by c , Add the Column — Repeat Now the engine runs. Take the number you just landed in the result row, multiply it by c , and write the product up in the next column. Add that column top-to-bottom. The sum lands in the result row — and becomes the next number to multiply. March this multiply ↗ then add ↓ cycle across every column. multiply the last result by c → → add down the column for the next result Result so far , carried up into the next column's middle row. Top coefficient + carried product = the new result-row entry. That new entry feeds the next multiply. Step one column right and repeat. When the last column is added, the final sum is the remainder . Bring down 2 . Then , and -6 + 4 = -2 . Next , and 2 + (-4) = -2 . Finally , and -1 + (-4) = -5 . Bottom row: . 4. Read Off the Quotient and Remainder

This is the written version of the interactive lesson above. See the full Pre-Calculus course.