Polynomial division

Math

Definition

The process of dividing one polynomial by another, producing a quotient and possibly a remainder. Long division and synthetic division are the two main methods.

How It Works

  1. Arrange both polynomials in descending order of degree
  2. Divide the leading term of the dividend by the leading term of the divisor
  3. Multiply the entire divisor by that result and subtract
  4. Bring down the next term and repeat until the remainder has lower degree than the divisor
  5. Write the answer as quotient + remainder/divisor

Examples

  • (x³ + 2x² - 5x + 1) ÷ (x - 2) using long division
  • Using synthetic division to divide by (x - 3)
  • Finding factors of a polynomial by dividing out known zeros
Key Fact

Remainder Theorem: when dividing f(x) by (x - c), the remainder equals f(c)

Related Terms

Polynomial operations Zeros and multiplicity Fundamental theorem of algebra Multiplying polynomials

Study This Concept

Practice polynomial division with free review games in these units:

Algebra 2 Unit 4: Polynomial Functions