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Algebraic (polynomial) division divides one polynomial by another to find a quotient and remainder, using long division or inspection. It underpins the factor and remainder theorems and partial fractions. It appears across A-Level and iAL Pure Maths with the major exam boards. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
Use long division or compare coefficients, keeping powers lined up and writing in zero terms for anything missing. The answer is the quotient plus the remainder over the divisor. Comparing coefficients is often faster once you know the shape of the answer.
Before you start
The groundwork here is the factor theorem and long division. This is the foundation for partial fractions and improper fractions. This sits in Pure 2.
What you learn
Polynomial long division — the same ‘bus-stop’ method as with numbers. It gives the quotient and any remainder, handles missing terms and non-monic divisors, and — paired with a known factor — lets you factorise and solve. Higher-degree dividends work exactly the same way — the key is to write a zero placeholder for every missing power so the columns stay aligned all the way down. The course works through division with a remainder, missing terms & quartics and factorise & solve via division. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Algebraic Division is part of the Algebra strand of our free A-level maths courses, studied in the AS year. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. Related topics students usually take next include Algebraic Fractions, Completing the Square, Composite and Inverse Functions, Factor & Remainder Theorem and Functions - Domain and Range. You can drill this strand further on the Algebra revision engine, with your accuracy saved to your skill tree.
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