Algebra - Division

Polynomials - Algebraic Long Division


Section 1 - Introduction And Examples
Videos Of Different Cases And Levels Of Difficulty

Section 2 - waldomaths.com
Step By Step Interactive Demonstrations

Section 3 - Alternative Presentation
With Different Placement Of Answer In Method


Section 1 - Introduction And Examples

Algebraic Long Division - Introduction
This video shows division with numbers using short division
and then does the same question with numbers to show long division
This long division method is then applied to algebraic division
The example shown is 3x3 - 5x2 + 8x - 4 divided by x - 2


The next video shows x3 - 2x2 - 13x + 6 divided by x + 3



Algebraic Long Division - An Example With A Missing Term
The example shown is x3 + 5x - 6 divided by x - 1
which is then written as x3 + 0x2 + 5x - 6 divided by x - 1



Algebraic Long Division
An Example With A Missing Term And A Remainder
The example shown is x3 + 2x2 - 3 divided by x - 2
which is then written as x3 + 2x2 + 0x - 3 divided by x - 2



Algebraic Long Division
With A Missing Term In Both Parts Of The Division And A Remainder
The example shown is x3 + 4x + 6 divided by x2 + 1
which is then written as x3 + 0x2 + 4x + 6 divided by x2 + 0x + 1



Algebraic Long Division
A More Difficult Example With A Missing Term And A Remainder
The example shown is x4 - x2 + x - 4 divided by x2 - 2x + 5
which is then written as x4 + 0x3 - x2 + x - 4 divided by x2 - 2x + 5





Section 1 - Introduction And Examples
Videos Of Different Cases And Levels Of Difficulty

Section 2 - waldomaths.com
Step By Step Interactive Demonstrations

Section 3 - Alternative Presentation
With Different Placement Of Answer In Method


Section 2 - waldomaths.com
Step By Step Interactive Demonstrations

waldomaths.com - Algebraic Long Division
Step By Step Interactive Display Of Computer Generated Questions

This video shows the operation of the interactive unit on waldomaths.com

Different options and levels are available on the links given here
EXTERNAL LINK waldomaths.com - Algebraic Long Division - Step By Step - Level 1
EXTERNAL LINK waldomaths.com - Algebraic Long Division - Step By Step - Level 2
The unit will generates a question and you can click to see the next step





Section 1 - Introduction And Examples
Videos Of Different Cases And Levels Of Difficulty

Section 2 - waldomaths.com
Step By Step Interactive Demonstrations

Section 3 - Alternative Presentation
With Different Placement Of Answer In Method


Section 3 - Alternative Presentation
Different Placement Of Answer In Method

Slightly Different Alternative Presentation:
Where The Answer Is Put In A Different Way In The Columns
It Starts In The Correct Column
For The Power Of The First Term In The Answer
The example shown is x3 - 12x2 + 44x - 48 divided by x - 2



A Quadratic Expression
Divided By A Linear Expression

x 2 + 2x + 1       divided by      x + 1

                      x + 1
x + 1 ) x2 + 2x + 1
             x2 + 1x
                      x + 1
                      x + 1
                      0 + 0

x2 + 2x + 1 = (x + 1)(x + 1) = (x + 1)2


A Cubic Expression
Divided By A Linear Expression

x3 + 2x2 + 2x + 1       divided by      x + 1

                     x 2 +   x + 1
x + 1 ) x3 + 2x2 + 2x + 1
             x3 + 1x2
                      x2 + 2x
                      x2 +   x
                                x + 1
                                x + 1
                                0 + 0

x3 + 2x2 + 2x + 1 = (x2 +   x + 1)(x + 1)

This will not factorise further


A Cubic Expression Without An x2 Term
Divided By A Linear Expression
And leaving A Remainder

3x3 + 2x + 1       divided by      x + 1

REWRITE AS

3x3 + 0x2 + 2x + 1       divided by      x + 1

                      3x 2 - 3x + 5 remainder - 4
x + 1 ) 3x3 + 0x2 + 2x + 1
             3x3 + 3x2
                    - 3x2 + 2x
                    - 3x2 -  3x
                            + 5x + 1
                            + 5x + 5
                                 0  - 4

x + 1 is not a factor of 3x3 + 2x + 1
because 3x3 + 2x + 1 does not divide by  x + 1
without leaving a remainder



Section 1 - Introduction And Examples
Videos Of Different Cases And Levels Of Difficulty

Section 2 - waldomaths.com
Step By Step Interactive Demonstrations

Section 3 - Alternative Presentation
With Different Placement Of Answer In Method


 

 

 




Section 1
Introduction And Examples
Videos Of Different Cases
And Levels Of Difficulty

Section 2 - waldomaths.com
Step By Step
Interactive Demonstrations

Section 3
Alternative Presentation
With Different Placement
Of Answer In Method

Edited by Dr David Cornelius an Independent Private Maths Tutor with over 25 years of experience and The Secretary of The Association of Tutors in the UK for 15 years.