Polynomial Division
6-7Polynomial Long Division
Overview
Divide polynomials by polynomials using long division, just like with whole numbers.
Key ideas
- Arrange both polynomials in descending order; fill missing terms with 0.
- Divide leading terms; multiply, subtract, bring down.
- Stop when the remainder’s degree is less than the divisor’s.
Worked examples
Example 1
Problem. Divide (x^2 + 5x + 6) by (x + 2).
Solution. Quotient x + 3, remainder 0. So result = x + 3.
Practice
Try each one. Click Show answer when ready.
- 1.
Divide (x^2 + 7x + 12) ÷ (x + 3).
- 2.
Divide (x^2 − 9) ÷ (x − 3).
- 3.
Divide (2x^2 + 7x + 3) ÷ (x + 3).
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Divide: (x³ + 2x² − 5x − 6) ÷ (x + 1).
- 2.
Divide: (2x³ − 5x² + 3x − 1) ÷ (x − 2).