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Study Guides > College Algebra

Key Concepts & Glossary

Key Equations

Division Algorithm f(x)=d(x)q(x)+r(x)f\left(x\right)=d\left(x\right)q\left(x\right)+r\left(x\right) where q(x)0q\left(x\right)\ne 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 in 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)f\left(x\right) and a non-zero polynomial divisor d(x)d\left(x\right) where the degree of d(x)d\left(x\right) is less than or equal to the degree of f(x),f\left(x\right), there exist unique polynomials q(x)q\left(x\right) and r(x)r\left(x\right) such that f(x)=d(x)q(x)+r(x)f\left(x\right)=d\left(x\right)q\left(x\right)+r\left(x\right) where q(x)q\left(x\right) is the quotient and r(x)r\left(x\right) is the remainder. The remainder is either equal to zero or has degree strictly less than d(x).d\left(x\right).
synthetic division
a shortcut method that can be used to divide a polynomial by a binomial of the form x k

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