Polynomial DivisionPractise dividing one algebraic expression by another in this set of exercises. 
This is level 5: mixed exercise from old textbook. This long, difficult exercise is only included here as a challenge for the very adventurous. The real challenge is being able to type in the answers so that they exactly match the answers given at the back of the ancient textbook this exercise was taken from (A First Book in Algebra, by Wallace C. Boyden written in 1895)
Did you know that there is a method for finding the remainder without having to do long division? It is called:
If a polynomial \(f(x)\) is divided by \((xa)\) 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.
InstructionsTry 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. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file. 



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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician? Comment recorded on the 9 April 'Starter of the Day' page by Jan, South Canterbury: "Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you." Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay: "An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!" 
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Go MathsLearning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school. Maths MapAre you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.  
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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/Alevel exam paper questions (worked solutions are available for Transum subscribers).
More Algebra including lesson Starters, visual aids, investigations and selfmarking exercises.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
See the National Curriculum page for links to related online activities and resources.
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.
Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can doubleclick the 'Check' button to make it float at the bottom of your screen.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
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