Polynomial Division

Practise dividing one algebraic expression by another in this set of exercises.

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This is level 1: divide a polynomial by a single term.

 1 $$\frac{2a^3-a^2}{a}$$ = 2 $$\frac{42a^5-6a^2}{6a}$$ = 3 $$\frac{21x^4+3x^2}{3x^2}$$ = 4 $$\frac{35m^4-7p^2}{7}$$ = 5 $$\frac{27x^5-45x^4}{9x^2}$$ = 6 $$\frac{24x^6-8x^3}{-8x^3}$$ = 7 $$\frac{34x^3-51x^2}{17x}$$ = 8 $$\frac{5x^5-10x^3}{-5x^3}$$ = 9 $$\frac{-3a^2-6ac}{-3a}$$ = 10 $$\frac{-5x^3+x^2y}{-x^2}$$ = 11 $$\frac{2a^5x^3-2a^4x^2}{2a^4x^2}$$ = 12 $$\frac{-x^2y-x^2y^2}{-xy}$$ = 13 $$\frac{9a-12b+6c}{-3}$$ = 14 $$\frac{a^3b^2-a^2b^5-a^4b^2}{a^2b}$$ = 15 $$\frac{3x^3-6x^2y-9xy^2}{3x}$$ = 16 $$\frac{x^2y^2-x^3y-xy^3}{xy}$$ = 17 $$\frac{a^3-a^2b-ab^2}{-a}$$ = 18 $$\frac{a^2b-ab+ab^2}{-ab}$$ = 19 $$\frac{xy-x^2y^2+x^3y^3}{-xy}$$ = 20 $$\frac{-x^6-2x^5-x^4}{-x^4}$$ = 21 $$\frac{a^2x-abx-acx}{ax}$$ = 22 $$\frac{3x^5y^2-3x^4y^3-3x^2y^4}{3x^2y^2}$$ = 23 $$\frac{a^2b^2-2ab-3ab^3}{ab}$$ = 24 $$\frac{4a^3c^3+8a^2c-12ac^2}{4ac}$$ =
Check

Did you know that there is a method for finding the remainder without having to do long division? It is called:

The Remainder Theorem

If a polynomial $$f(x)$$ is divided by $$(x-a)$$ then the remainder is $$f(a)$$

Do some independent research to find out more about this theorem and how it can be used to complete this exercise really quickly.

You may be interested to know that students were answering these very same questions over one hundred years ago. This exercise comes from a textbook written in the 1890s.

This is Polynomial Division level 1. You can also try:
Level 2 Level 3 Level 4 Level 5

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

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Description of Levels

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Algebraic Fractions - For a simpler introduction have a go at Algebraic Fractions level 1.

Level 1 - Divide a polynomial by a single term

Level 2 - Divide a polynomial by a linear expression

Level 3 - Find the remainder

Level 4 - Divide a polynomial by a quadratic or cubic expression

Level 5 - Mixed exercise from old textbook

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Algebra including lesson Starters, visual aids, investigations and self-marking exercises.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Divident ÷ Divisor = Quotient

To type indices or exponents use the up arrow key ^ then type the number followed by the right arrow. The terms in your answer should be in the same order as the terms in the question.

Beth's Method (see video above)

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Typing Mathematical Notation

These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.

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