Polynomial long division works like number long division: divide the leading term, multiply, subtract, bring down. If P(x) ÷ D(x) = Q(x) remainder R(x), then P(x) = D(x)·Q(x) + R(x). By the factor theorem, if P(a) = 0, then (x−a) is a factor of P(x).
How to Use
Enter polynomial coefficients:
- Dividend: Coefficients highest to lowest
- Divisor: Coefficients of divisor
- Result: Quotient and remainder
Synthetic Division
When dividing by (x−c), synthetic division is faster. Only use the coefficients and the value c. Bring down, multiply, add, repeat.
Factor Theorem
If P(c)=0, then (x−c) divides P(x) evenly (remainder 0). This helps find roots: test small integers as potential zeros.
Step-by-Step Instructions
- 1Enter dividend coefficients.
- 2Enter divisor coefficients.
- 3View quotient and remainder.
- 4Check if divisor is a factor.
- 5Review step-by-step process.