Polynomial Long Division
Divide polynomials like integers to find quotient and remainder.
Key idea
Divide polynomials like integers to find quotient and remainder.
In depth
Divide polynomials like numbers: divide leading terms, multiply, subtract, bring down. You obtain a quotient and remainder, with dividend = divisor × quotient + remainder.
Worked example
(x² + 5x + 6) ÷ (x + 2): x → subtract x² + 2x → 3x + 6; 3 → quotient x + 3, remainder 0.
Real-world uses
- Factoring higher-degree polynomials in control systems and simplifying rational functions
Common mistake
Leaving out a missing power. Include 0x² as a placeholder.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Polynomial Long Division?
Divide polynomials like integers to find quotient and remainder. It is a topic at the advanced level in Algebra.
Where is Polynomial Long Division used in real life?
Real-world examples: Factoring higher-degree polynomials in control systems and simplifying rational functions.
What should I learn before Polynomial Long Division?
Make sure you are comfortable with Polynomial Functions and Graphs, the previous topic in Algebra.
What is a common mistake with Polynomial Long Division?
Leaving out a missing power. Include 0x² as a placeholder.
How can I practise Polynomial Long Division?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Polynomial Long Division?
Move on to Synthetic Division next.
Related advanced topics in Algebra
- Absolute Value Inequalities – Rewrite as a compound inequality.
- Systems with Three Variables – Reduce to two variables then solve in sequence.
- Systems of Inequalities – Solution region is the overlap of half-planes.
- Factoring by Grouping – Group terms in pairs to find a common binomial.
- Sum and Difference of Cubes – Special factoring patterns for cubes.
- Completing the Square – Rewrite a quadratic as a perfect square plus constant.