Summary: Dividing Polynomials

Key Equations

Division Algorithm f(x)=d(x)q(x)+r(x) where q(x)0

Key Concepts

  • Polynomial long division can be used to divide a polynomial by any polynomial with equal or lower degree.
  • The Division Algorithm tells us that a polynomial dividend can be written as the product of the divisor and the quotient added to the remainder.
  • Synthetic division is a shortcut that can be used to divide a polynomial by a binomial of the form x – k.
  • Polynomial division can be used to solve application problems, including area and volume.

Glossary

Division Algorithm
given a polynomial dividend f(x) and a non-zero polynomial divisor d(x) where the degree of d(x) is less than or equal to the degree of f(x), there exist unique polynomials q(x) and r(x) such that f(x)=d(x)q(x)+r(x) where q(x) is the quotient and r(x) is the remainder. The remainder is either equal to zero or has degree strictly less than d(x).
synthetic division
a shortcut method that can be used to divide a polynomial by a binomial of the form x k