3.3 Long and Synthetic Division

Notes

Divide polynomials like numbers: $\displaystyle \frac{\text{dividend}}{\text{divisor}} = \text{quotient} + \frac{\text{remainder}}{\text{divisor}}$.

• Long division works for any divisor. Fill in missing powers with 0 terms.
• Synthetic division is a shortcut when dividing by $x - c$. Use $c$ (so for $x + 2$, use $-2$).
• Synthetic steps: bring down the first coefficient, multiply by $c$, add to the next coefficient, repeat. The last number is the remainder.
• Example: $(x^2 + 7x + 10) \div (x + 2) = x + 5$, remainder 0.