Geometry.Net - Basic_P: Polynomial Division

Polynomial Expressions
The polynomial division and remainder are done using the defined monomial orderin the base ring. Parentheses are used to enforce groupings in an expression.
http://www.math.columbia.edu/online/Macaulay1-rel0994-html/node22.html

Extractions: Next: Integer lists Up: Input Syntax Previous: Integer Expressions The syntax for polynomial expressions is similar to integer expressions. The legal operators for polynomials, in order of increasing precedence, are given in the following table. The polynomial division and remainder are done using the defined monomial order in the base ring. Parentheses are used to enforce groupings in an expression. The following remarks describe certain aspects of polynomial expressions. Polynomials in Macaulay are output in an abbreviated notation: each polynomial is displayed as a number of monomials separated by ``+'' or ``-''. Each monomial is preceeded by its coefficient and each indeterminate is followed by its degree with no intervening blanks. Rational number coefficients are represented by x y . A polynomial which extends over a line boundary is displayed by using as the continuation character. If you wish to have polynomials output in Mathematica format, use the prmat command.
Honors Algebra II
Have a polynomial division duel. Two students will simultaneously work the same problem;one doing polynomial division while the other uses synthetic division.
http://www.hccsc.k12.in.us/curriculum/Honors Algebra II.htm

Extractions: HUNTINGTON NORTH HIGH SCHOOL HONORS ALGEBRA II CURRICULUM NOVEMBER, 1998 PROFICIENCY OBJECTIVES ACTIVITIES ASSESSMENT 1)Develop and Apply the Understanding of Algebraic Concepts and Skills to Solve Equations and Inequalities. Students will: 1)solve and graph linear equations and inequalities. 2)interpret the slope and intercepts of a line. 3)learn to write equations in point-slope, slope-intercept, and standard form. 4)graph absolute value inequalities by recognizing conjunctions and disjuctions. 5)graph and solve systems of equations and inequalities. Have students make up word sentence equations or inequalities. Trade and solve each others. As an application of slope, students will measure the rise and tread of various flights of stairs and record their measurements in a table. Research the federal guidelines for the slope of a handicapped ramp. Design a ramp to replace steps around town. Using graphing calculators, have students graph systems of equations. Divide students into groups of three. On the same graph, each student will graph an inequality and shade it in a different color. They will highlight the solution of all three inequalities with a fourth color.
Matlab Commands List
ctrb, The controllability matrix, see also obsv. deconv, Deconvolution andpolynomial division, see also conv. det, Find the determinant of a matrix.
http://www.engin.umich.edu/group/ctm/extras/commands.html

Extractions: Matlab Commands List The following list of commands can be very useful for future reference. Use "help " in Matlab for more information on how to use the commands. In these tutorials, we use commands both from Matlab and from the Control Systems Toolbox, as well as some commands/functions which we wrote ourselves. For those commands/functions which are not standard in Matlab, we give links to their descriptions. For more information on writing Matlab functions, see the function page. Note :Matlab commands from the control system toolbox are highlighted in red Non-standard Matlab commands are highlighted in green Command Description abs Absolute value acker Compute the K matrix to place the poles of A-BK, see also place axis Set the scale of the current plot, see also plot, figure bode Draw the Bode plot, see also logspace, margin Continuous system to discrete system clf Clear figure (use clg in Matlab 3.5) conv Convolution (useful for multiplying polynomials), see also deconv ctrb The controllability matrix, see also obsv deconv Deconvolution and polynomial division, see also conv
Synthetic Division
Author James White. Suggested Use Study algebra of polynomial division. Topicscollege algebra, polynomials, gcd, synthetic division, symbolic algebra.
http://www.mathwright.com/book_pgs/book055.html

Extractions: Been away for a while? Check out our new building by clicking the picture on the right! This WorkBook requires Mathwright Library Player 2000 to read it. To download the book, press the button on the left. A self-extracting file will be downloaded. Either save it to disk and execute it later, or simply select "Open it" from the popup dialog. This places the book, along with its documentation, on the Start, Programs, Mathwright Library menu, so that you may read it whenever you like. Size: 131 KB Find similar WorkBooks in the Rooms below: Categories: Home Study Tools Math and Computers Subjects: Algebra College Algebra Precalculus Factorization ... Rational Functions Title: Synthetic Division Book Description: In this command-line WorkBook, students may explore synthetic division of polynomials with rational coefficients. There is a command called Synthetic that returns the quotient of one polynomial by another (with rational coefficients) together with the remainder part. There are also several programs that support exploration. These are: Divide(num,den) returns the same result that synthetic would. This result can then be used by another command (for example, to define a function and draw its graph). Pquotient and Premainder returns the results (quotient and remainder) from the Euclidean algorithm. Finally, GCD returns the greatest common divisor of two rational polynomials.
Algebra Cheat 2
Program solves variable equations and gives explanations of steps used.Category Science Math Algebra Software shown. A great tool for polynomial multiplication, Algebra Cheat 1is even capable of polynomial division, try it and see. To help
http://www.bacsoftware.co.uk/algebra/

Extractions: Algebra Cheat 2 Simplifies any algebraic expression, Solves Simple Equations, Solves Quadratic Equations and Solves Simultaneous equations. A great tool for polynomial multiplication, Algebra Cheat 2 is even capable of polynomial division, try it and see. To help you learn and understand Algebra, Algebra Cheat 2 also provides a full and detailed explanation of how the simplification or solution of an equation was done. Click for full size Algebra Cheat 2 Features List Simplify any Algebra expression Simplify any Algebra equation Addition and Subtraction of any algebra expressions Multiplication of any algebra expressions Addition and Subtraction of any polynomials Multiplication and Division of any Polynomials Solves any simple linear equation Solves Simultaneous linear equations of up to 5 variables Solves any quadratic equation of one variable Factorises quadratic equations of one variable Detailed explanation of Solution Algebra Cheat 2 is shareware and costs GB £20.00 to register a copy, which converts to about US $29.00.
The Cyclic Redundancy Check
The presentation of the CRC is based on two simple but not quite everyday bitsof mathematics polynomial division. polynomial division isn't too bad either.
http://www.cs.jhu.edu/~scheideler/courses/600.344_S02/CRC.html

Extractions: Taken from lecture notes by Otfried Schwarzkopf, Williams College. A significant role of the Data Link layer is to convert the potentially unreliable physical link between two machines into an apparently very reliable link. This is done by including redundant information in each transmitted frame. Depending on the nature of the link and the data one can either: Most current networks take the former approach. One widely used parity bit based error detection scheme is the cyclic redundancy check or CRC. The CRC is based on some fairly impressive looking mathematics. It is helpful as you deal with its mathematical description that you recall that it is ultimately just a way to use parity bits. The presentation of the CRC is based on two simple but not quite "everyday" bits of mathematics: polynomial division arithmetic over the field of integers mod 2.
Math Forum - Ask Dr. Math
Once you understand how polynomial division works, you can write it like this b^6+2b^3 + b+1 b^3+4 ) b^9+0b^8+0b
http://mathforum.org/library/drmath/view/56437.html

Extractions: Associated Topics Dr. Math Home Search Dr. Math Date: 12/03/2001 at 11:54:18 From: Rachel Subject: Dividing a Polynomial by a Polynomial using long division b^9+6b^6+b^4+9b^3+4b+8 by b^3+4 Why in some questions do you need to add place holders? It has something to do with ascending and descending powers. I am homeschooled and someone said that this was a great site. Please help! http://mathforum.org/dr.math/ Associated Topics
College Algebra: Graphs And Models Chapter 3 -- InterAct Math Tutorials
Problem 51. Exercise Set 3.2 polynomial division; The Remainder andFactor Theorems. Problem 1, Problem 3, Problem 5, Problem 7, Problem9.
http://occawlonline.pearsoned.com/bookbind/pubbooks/bittinger10_awl/chapter3/cus

Extractions: Practice with our InterAct Math tutorial exercises over the Web! To use the InterAct Math tutorials over the web, you will need to download and install the InterAct Math Plugin for Windows. Click the Download InterAct Math button for complete instructions. You will only need to install the plugin once. Exercise Set 3.1: Polynomial Functions and Modeling Exercise Set 3.5: Polynomial and Rational Inequalities Problem 1 Problem 3 Problem 5 Problem 7 ... Problem 51 Problem 1 Problem 3 Problem 5 Problem 7 ... Problem 35 Problem 1 Problem 3 Problem 5 Problem 7 ... Problem 55 Problem 1 Problem 3 Problem 5 Problem 7 ... Problem 49 Problem 1 Problem 3 Problem 5 Problem 7 ...
Mr. Specht TeacherWeb Assignments
Assign 313 pg 313 January 24 Friday Prealgebra- Chapter Review 130-132 Algebra 1A-Multi-step Equations p169 7-24 Algebra 1B- polynomial division Assign 27-40
http://teacherweb.com/or/hillsboro/specht/h2.stm
Finite Differences On A Helix
deconvolution. Using in onedimensional polynomial division, we cansolve many formerly difficult problems very rapidly. Consider
http://sep.stanford.edu/sep/jon/optical/paper_html/node5.html

Extractions: Next: Matrix view of the Up: Multidimensional recursive filters via Previous: Examples of simple 2-d The function is an autocorrelation function. It is symmetrical about the ``4'' and its Fourier transform is positive for all frequencies. Digging out an old textbook Claerbout (1976) , we discover how to compute a causal wavelet with this autocorrelation. I used the ``Kolmogoroff spectral-factorization method'' to find this wavelet Wind the signal around a vertical-axis helix to see its two-dimensional shape This 2-D filter is is the negative of the finite-difference representation of the negative of the Laplacian operator, generally denoted .Now wind the signal around the same helix to see its two-dimensional shape In the 2-D representation ( ) we see the coefficients diminishing rapidly away from maximum value 1.791. My claim is that the 2-D autocorrelation of ( ) is ( ). You verified this idea at the beginning of this paper where the numbers were all ones. You can check it again in a few moments if you drop the small values, say 0.2 and smaller. Since the autocorrelation of is is a second derivative, the operator
Calendar/Syllabus
3.1, Polynomial functions, 112,14,16,17,21,36, UG. 3.2,polynomial division, 1-8,29,30 (no synthetic division
http://www.math.uri.edu/Courses/spring03/mth111/calendar_syllabus.htm
File Verification Using CRC
CRC calculations are done using a technique with the formidable nameof polynomial division . A block of data, regardless os how
http://dogma.net/markn/articles/crcman/crcman.htm

Extractions: Recently I have found myself thinking a lot about file verification. By file verification, I mean the process of determining whether a file on my computer has been modified unexpectedly. Whether it happened through hardware failure, program error, or malicious tampering, I like to know when a file has had its contents altered. Likewise, I would like a convenient way to check the integrity of a file to verify that it hasn't been changed. The problem of file integrity has been on my mind because of several nearly simultaneous incidents. First of all, I recently ran dozens of relatively untested programs through my home systems while I was judging the Dr. Dobb's Data Compression Contest. At least two of these programs caused inadvertent damage to the file systems on my computer, one under UNIX and one under MS-DOS. In both cases, I was able to spot a lot of the damage, but after I restored the data that looked bad, I was left feeling unsure about the rest of my system. Had other files been damaged in more subtle ways? I suddenly felt as though I couldn't trust my system. An even more alarming incident occurred a couple of weeks later. A programmer who supplies us with a product for resale called us up and casually mentioned that his office had been infested with the notorious "Stoned" virus. Had we by any chance noticed anything funny in oursystems? We see funny things on our systems on an hourly basis, sosuddenly we were once again in the position of not trusting any of the files on our computers. (Fortunately this turned out to be a false alarm).
Videos And Print
Tape 9 Quadratic Functions, Polynomial Functions of Higher Degree. Tape 10 -polynomial division, Synthetic Division, Real Zeros of Polynomial Functions.
http://www.pserie.psu.edu/learnctr/videos.htm
DMTCS SERIES
An Introduction to Polynomials Construction and representation of polynomials; Complexityand cost; polynomial division; Polynomial factorization; Polynomial
http://www.cs.auckland.ac.nz/CDMTCS/docs/mignotte.html

Extractions: M. Mignotte, D. Stefanescu. Polynomials. An Algorithmic Approach, Springer-Verlag, Singapore, 1999. Approx. 320pp. ISBN: 981-4021-51-2. US$49 softcover. This textbook gives a well-balanced presentation of the classic procedures of polynomial algebra which are computationally relevant and some algorithms developed during the last decade. The first chapter discusses the constrcution and the representation of polynomials. The second chapter focuses on the computational aspects of the analytical theory of polynomials. Polynomials with coefficients in a finaite field are then described in chapetr three, and the final chapter is devoted to factorization of polynomials with integral coefficients. The book is primarily aimed at graduate students taking courses in Polynomial Algebra, with a prerequisite knowledge of set theory, usual fields and basic algebra. Fully worked out examples, hints and references complement the main text, and details concerning the implementation of algorithms as well as indicators of their efficiency are provided. The book is also useful as a supplementary text for courses in scientific computing, analysis of algorithms, computational polynomial factorization, and computational geometry of polynomials. Contents: 1. An Introduction to Polynomials: Construction and representation of polynomials; Complexity and cost; Polynomial division; Polynomial factorization; Polynomial roots. Eliminations. Resultants; Symmetric functions; Polynomial interpolation; Irreducinility criteria. 2. Complex Polynomials: Polynomial size; Geometry of polynomials; Stable polynomials; Polynomial roots inside the unit disk; Bounds for the roots; Applications to integer polynomials; Separation of roots. 3. Polynomials with Coefficients in a Finite Field: Finite fields; Cyclotomic polynomials; Fast Fourier transform; Number of irreducible polynomials over a finite field; Constrcution of irreducible polynomials over a finite field; Roots of polynomials over finite fields; Squarefree polynomials; Berlekamp's algorithm; Niederreiter's algorithm. 4. Integer Polynomials: Kronecker's factorization method; The berlekamp-Zassenhaus algorithm; The LLL factorization algorithm. Bibliography; Notation; List of Algorithms; Index.
Citation
SIAM Journal on Computing archive Volume 22 , Issue 3 (June 1993) toc Improvedparallel polynomial division Authors Dario Bini Victor Pan Publisher Society
http://portal.acm.org/citation.cfm?id=152040&dl=ACM&coll=portal&CFID=11111111&CF
Nelson Thornes Online Education
Leibniz. polynomial division This site gives some worked examplesof polynomial division and advice about checking answers. There
http://www.nelsonthornes.com/secondary/maths/16_links.htm
3.3 - Real Zeros Of Polynomial Functions
One key point about division, and this works for real numbers aswell as for polynomial division, needs to be pointed out. When
http://www.richland.cc.il.us/james/lecture/m116/polynomials/zeros.html

Extractions: You were taught long division of polynomials in Intermediate Algebra. Basically, the procedure is carried out like long division of real numbers. The procedure is explained in the textbook if you're not familiar with it. One key point about division, and this works for real numbers as well as for polynomial division, needs to be pointed out. When you divide the dividend by the divisor, you get a quotient and a remainder. To check the problem, you multiply the divisor by the quotient and add the remainder to get the dividend. If the remainder is 0, then we say that the divisor divides evenly into the dividend. Like I said, the same thing can be done with polynomial functions. f(x) = d(x) * q(x) + r(x) Where f(x) is the polynomial function being divided into (dividend), d(x) is the polynomial function being divided by (divisor), q(x) is the polynomial function that is the quotient, and r(x) is the polynomial remainder function and will have degree less than the divisor. If the remainder, r(x), is zero, then f(x) = d(x)*q(x). We have just factored the function f(x) into two factors, d(x) and q(x).
ThinkQuest Library Of Entries
polynomial Functions. Synthetic division ex. divide (2x 4 5x 3+ 7x 2 + 3x + 2) by (x - 3). In the divisor, use 3 instead of -3
http://library.thinkquest.org/10030/8syndiv.htm

Extractions: The web site you have requested, Seeing is Believing , is one of over 4000 student created entries in our Library. Before using our Library, please be sure that you have read and agreed to our To learn more about ThinkQuest. You can browse other ThinkQuest Library Entries To proceed to Seeing is Believing click here Back to the Previous Page The Site you have Requested ... click here to view this site Click image for the Site Languages : Site Desciption Need a primer on math, science, technology, education, or art, or just looking for a new Internet search engine? This catch-all site covers them all. Maybe you're doing your homework and need to quickly look up a basic term? Here you'll find a brief yet concise reference source for all these topics. And if you're still not sure what's here, use the search feature to scan the entire site for your topic.
Untitled
ldiv polynomial matrix long division; numer numerator; pdiv polynomialdivision; pol2des polynomial matrix to descriptor form; pol2str
http://pauillac.inria.fr/cdrom/www/scilab/doc/manual/index8.html
Division Of A Polynomial By A Monomial
division OF A polynomial BY A MONOMIAL. division, like multiplication,may be distributive. division OF A polynomial BY A polynomial.
http://www.tpub.com/math1/10g.htm

Extractions: Click here to make tpub.com your Home Page Division of a polynomial by a monomial tpub.com Updates Back Home Up ... Next DIVISION OF A POLYNOMIAL BY A MONOMIAL Division, like multiplication, may be distributive. Consider, for example, the problem 2, which may be solved by adding the numbers within the parentheses and then dividing the total by 2. Thus, Now notice that the problem may also-be solved distributively. CAUTION: Do not confuse problems of the type just described with another type which is similar in appearance but not in final result. For example, in a problem such as 2 the beginner is tempted to divide 2 successively by 4, then 6, and then -2, as follows: Notice that we have canceled the "equals" sign, because 2 + 8 is obviously not equal to 1/2 + 2/6. - 1. The distributive method applies only in those cases in which several different numerators are to be used with the same denominator When literal numbers are present in an expression, the distributive method must be used, as in the following two problems: Quite often this division may be done mentally, and the intermediate steps need not be

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