Key Concepts & Glossary
Key Equations
Division Algorithm | [latex]f\left(x\right)=d\left(x\right)q\left(x\right)+r\left(x\right)[/latex] where [latex]q\left(x\right)\ne 0[/latex] |
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 [latex]f\left(x\right)[/latex] and a non-zero polynomial divisor [latex]d\left(x\right)[/latex] where the degree of [latex]d\left(x\right)[/latex] is less than or equal to the degree of [latex]f\left(x\right),[/latex] there exist unique polynomials [latex]q\left(x\right)[/latex] and [latex]r\left(x\right)[/latex] such that [latex]f\left(x\right)=d\left(x\right)q\left(x\right)+r\left(x\right)[/latex] where [latex]q\left(x\right)[/latex] is the quotient and [latex]r\left(x\right)[/latex] is the remainder. The remainder is either equal to zero or has degree strictly less than [latex]d\left(x\right).[/latex]
- synthetic division
- a shortcut method that can be used to divide a polynomial by a binomial of the form x – k
Licenses & Attributions
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- Precalculus. Provided by: OpenStax Authored by: Jay Abramson, et al.. Located at: https://openstax.org/books/precalculus/pages/1-introduction-to-functions. License: CC BY: Attribution. License terms: Download For Free at : http://cnx.org/contents/[email protected]..