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2:3 part 2 -- Long Division

Page history last edited by Math in a Box - Susan Johnsey gm 2 years, 1 month ago


Lesson 2.3 Part 2 Polynomial Divided by a Binomial


Example of Long Division: x4- 3x2+ 4x - 5 divided by x+2

Please note that if a term is "missing" such as the x3 in the problem above

              then we need to add a zero term for it  .

                              x4 + 0x3 - 3x2+ 4x - 5


We need a number term (constant) at the end.   We have one: - 5.


  IN MY LAST DIAGRAM of division below, its in a blue box.

Do you see that

     all the x4 terms are lined up in a column, (under each other)

and that

     all the x3 terms are also all lined up one under the other.

And then

     all the x2 terms are also lined up under each other.

     The x terms are under each other too!



There is a total of 6 "x-terms" in the last diagram and they are all in one column, (under each other).

Do you see them below ? count the 6 terms.


Each type of term must be written in the correct column as we work down the paper.  


Let's begin now with the first diagram.  

    NOTE the 0x3  term.  We must use 0 terms when one is missing.   We are missing the x3 term.


Begin by looking at the x and the x4.     

WRITE THESE EXAMPLE INTO your notes, following the directions as I give them.    Watch the video first, that is below, if you have never done this before.


When I ask you to multiply below we always multiply times the x+2.  Do you see it out front? 

LOOK AT ALL the details.   We divide, multiply, subtract and bring down.   The 4 steps for division that you have done since 4th grade.  But we are working with variables and exponents as well as numbers.  

Watch the multiply and the subtract!  Study those steps carefully.

Watch the video first, that is below, if you have never done this before.  Then come back to this Example.

 NOTE  HOW I HAVE KEPT THE LIKE TERMS LINED UP.   They must be done that way.   We can not add or subtract unlike terms.        


SEE how all the x2  terms are lined up under each other in the final diagram?  



Please copy this problem down. 

This is a lesson in algebra: divide-multiply-subtract - bringdown- . But also a lesson in organized, orderly writing.

SEE all the x terms are lined up under each other.



                     DO YOU SEE THE 6 "x-terms"   in a long column,   ALL under each other?

                        Do you  see how to LINE THE terms up as you go through the DIVISION process?




LOOK carefully how to write the final answer:        Formula 



The remainder is written as the numerator of the fractionand

 the divisor is the denominator.


Now you write this division problem down and do this by yourself.

You must do that . Just reading this is not enough. You must learn to write the problem.


There is only one example to learn. If you can WRITE every step of the above by yourself

and you understand the sign changes then you will be able to do your assignment.



Here is a VIDEO that shows you an example of dividing.

The first example is easy.

The second one or maybe it was the third  shows you how to use the "0 term"

I used it in my example above.


Copy and paste it into your address bar to go there.  It may have ads so click the little x or skip add





WATCH the subtractions closely. 

             DO NOT MISS the Subtractions.!!!


Do not try the assignment until you have done the one above more than once.

Do Assignment 2.3b


The video above is for the harder problems.    The video below is for the easier problems. 

So if you did not get those above then you really should watch this one and work these easier problems first.  Then try the harder ones again.


Video that will help with the easy long division:

There are 3 examples. Be sure you write down all three.  For the last example can you explain to me where she got the -6x and then later the -12 in her subtraction steps?

Be sure you know.

Or use this link to the video:






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