# synthetic division of polynomials

1. ## synthetic division of polynomials

hello
I am very new to excel and have used it a few times about ten years ago, nothing since then.
I have to make a spreadsheet that carries out synthetic division of polynomials.
this involves powers of X, which I can not find on the internet. I have looked on youtube but they only show basic division. I have put in different searches and cannot find anything that is helping. I know of the POWERS option in one of the drop down menus but don't know how to get X. also, I don't know how to display these things. how would I show this in a table?
any help would be greatly appreciated.
many thanks
simon

2. ## Re: synthetic division of polynomials

In cell A2: =A1^3
Is this what you mean?

3. ## Re: synthetic division of polynomials

Hi and welcome to the forum,

Am I right in thinking that you have a reasonable grasp of this topic (polynomial division) and that it's just the representation of that knowledge in Excel with which you're not so confident? (Though your statement that "this involves powers of X, which I can not find on the internet." has me a little concerned - are you suggesting that you are to perform complex polynomial division yet are not entirely sure what the power of a number is?)

If so, you may also appreciate that, for many members of the forum, the opposite is true, i.e. they are able and practised in the use of Excel, though may not have even heard of polynomial division.

Perhaps the best and most fruitful way forward would be for you to share your knowledge of this particular topic in mathematics, perhaps giving a few examples and illustrating the basic principles, and then hopefully someone with the spreadsheet knowledge can take your theories and translate them into the necessary logic required to develop solutions in Excel.

As a final comment, I should also add that, from the phrasing of your question, there appears to be a small chance that your query is homework-related, in which case I should let you know that it is not forum polcy to give out answers in such cases - guidance, perhaps, but not answers.

Regards

4. ## Re: synthetic division of polynomials

hello
first of all I would like to thank you for welcoming me!
and secondly for the fast reply!!

sorry for any confusion in the post, I can do synthetic division of polynomials just not in excel. I haven't got a clue about it!
I have done some searching and found an article in a magazine called "The Mathematical Gazette, Vol. 87, No. 510 (Nov., 2003)". from a brief look I think it covers all the things I need.
thank you very much
all the best!

5. ## Re: synthetic division of polynomials

hello
I read through that article I found and it does say something about synthetic division of polynomials and horners method when using spread sheets. how ever I am none the wiser and cannot find anything that shows exactly what I require for a pass on my HNC electronics course.

I understand synthetic division of polynomials but have no idea about putting this into a spread sheet. the article seemed really complicated. I don't know how to put in the unknown x or how to solve that. I tried entering it but some error comes up.
is there a good web page that shows the steps for entering algebra. I have looked and cant find anything that would suit this. I am going to use horners method and hopefully this will be acceptable. but I think they would want me to show the X values with the degree above it. I am not excellent at maths, the names of these things is a little confusing for me. I know how to do the formulas and show the working out. I don't know the names of some parts of the maths formulas. I would say x to the power 2 or x squared (that's x with a 2 at top right)

so yeah, web sites. if anyone knows of a step by step method that is fairly straight forward I would really appreciate it!

many thanks and all the best

simon

6. ## Re: synthetic division of polynomials

It has been a long time since I used synthetic division, so I had to refresh my memory. Wikipedia has a decent description http://en.wikipedia.org/wiki/Synthetic_division purplemath (http://www.purplemath.com/modules/synthdiv.htm) also has a decent tutorial for synthetic division that might be even easier to see how to put it into a spreadsheet. As easily as this should go into a spreadsheet, I have to wonder if there is something deeper behind your question (after all these years are you having difficulty remembering how to build formulas in spreadsheets?).

1) Following Wikipedia's first example, put the coefficients of the dividend in row 1 (starting in column B).
2) row 2 will be for the "multiplication" steps. column A will hold the divisor constant. columns C up will hold a simple multiplication formula =\$A\$2*B3 (note the use of the absolute reference so the formula can be copied across).
3) row 3 will hold the summation steps. =sum(b1:b2)

then adapt to more complex problems.

7. ## Re: synthetic division of polynomials

hello

I did an ecdl in 98-99 and haven't used it since. it did not cover synthetic division and I didn't practice that much. I just completed the basic assignments to finish the course.
now im studying for an HNC in electronic engineering and a requirement is showing synthetic division of polynomials in spread sheets. I have managed to get the basic formula sorted out. probably not as good as others but it seems to work. though when I enter a new value as the divisor it comes up as the date.
the problem now is getting is to show the X and the number above it. the answer is supposed to be one lower than the previous power. so if the first number had x to power 2 then the answer would be just x. if it were to power 4 then the answer would be 3. I haven't found a way of showing this. part of my course included dividing the x power by the x in the divisor, so x2 would be x and so on. I don't know how to do this. I was thinking about creating an answer area and just making the number appear under the correct x. if that makes sense?
anyway, powers of x now. does anyone know how to show the x's and their powers and include this in the formula. I have read that horners method makes this easier which I have done so far(I believe). but I would like to make it look like the actual answer.
I really appreciate the help
thanks
simon

8. ## Re: synthetic division of polynomials

It is possible to use the concatenate function or the "&" operator to build the desired text string. For polynomials, this is usually inadequate, because you cannot superscript a portion of a text string that is built by formula. If you can build the text string manually so you can enter it as a text literal, then you can superscript individual characters.

My personal preference is to have a table with a column for each term in the polynomial. The heading will show the power of x for that term and the table entry will show the coefficient:
``Please Login or Register  to view this content.``
When I decide that I must have a nice, algebraic text string for the function, I usually build the text string in a word processor (like Word), linking the appropriate elements of the formula to the appropriate cells in Excel. You could also use VBA (or other programming language) to build the text string, then paste it into a spreadsheet cell as a text literal and format the appropriate characters as superscript.

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