Polynomial long and synthetic division

Polynomial long and synthetic division

Build reliable polynomial division skills for precalculus: organize coefficients, include missing powers, subtract complete products, and interpret the quotient together with its remainder. The set connects long division, synthetic division and the polynomial division identity.

Practice includes linear and quadratic divisors, a dividend of smaller degree, reconstruction from a quotient and remainder, and scaling when a linear divisor is not monic. Error-analysis questions distinguish a valid division result from an unfinished calculation. Rational-expression interpretations retain excluded inputs.

Prerequisites are polynomial arithmetic, distribution, combining like terms and restrictions in rational expressions. Single-select and multiselect tasks progress from setup and calculation to checking identities and explaining why an algorithm applies. Every problem is self-contained.

Use scratch work before selecting a response. Verify a result by multiplying the divisor by the quotient and adding the remainder, then check the remainder's degree. Detailed explanations connect the calculation to the original expression. This practice supports later factor and remainder theorems without assuming them as shortcuts or claiming that a quiz score alone proves fluency.