21. Learn.co.uk - Learning Resources For The National Curriculum, Online Lessons, GC factors. Polynomials. polynomial division. The remainder theorem. Thefactor theorem. polynomial division, The Euclidean property. If http://www.learn.co.uk/default.asp?WCI=Unit&WCU=27255

22. Polynomial Division First Previous Next Last Index Home Text. Slide 18 of 26. http://www.cs.berkeley.edu/~kfall/EE122/lec06/sld018.htm

23. Polynomial Division polynomial division. 10011010000. 1101. 1. 1101. 1001. 1101.1. 1000. 1101. 1011. 1101. 1. 1. 1. 0. 0. 1. 1100. 1101.1000. 1101. 101. http://www.cs.berkeley.edu/~kfall/EE122/lec06/tsld018.htm

Polynomial Division Previous slide Next slide Back to first slide View graphic version

24. Pdiv: ----- Polynomial Division 2.7.24 pdiv polynomial division. Elementwise euclidan division of thepolynomial matrix P1 by the polynomial P2 or by the polynomial matrix P2. http://scilabsoft.inria.fr/doc/manual/Docu-html775.html

2.7.24 pdiv: - polynomial division CALLING SEQUENCE [R,Q]=pdiv(P1,P2) [Q]=pdiv(P1,P2) PARAMETERS : polynomial matrix : polynomial or polynomial matrix R,Q : two polynomial matrices DESCRIPTION Element-wise euclidan division of the polynomial matrix by the polynomial or by the polynomial matrix Rij is the matrix of remainders, Qij is the matrix of quotients and P1ij = Qij*P2 + Qij or P1ij = Qij*P2ij + Qij EXAMPLE x=poly(0,'x'); p1=(1+x^2)*(1-x);p2=1-x; [r,q]=pdiv(p1,p2) p2*q-p1 p2=1+x; [r,q]=pdiv(p1,p2) p2*q+r-p1 SEE ALSO ldiv gcd

25. Detailed Information For Polynomial Division Program Simple programto divide polynomials. Authors Eliel Louzoun Mikael Sundstrom.......polynomial division Program. Filename polydiv.zip. http://www.hpcalc.org/details.php?id=357

26. Polynomial Division By Ewen Miller polynomial division by Ewen Miller. reply to this message post a messageon a new topic Back to sci.math.symbolic Subject Polynomial http://mathforum.org/epigone/sci.math.symbolic/bruzaxjand

Polynomial Division by Ewen Miller reply to this message post a message on a new topic Back to sci.math.symbolic Subject: Polynomial Division Author: ewenmiller@hotmail.com Organization: http://groups.google.com/ Date: The Math Forum

27. Polynomial Division a topic from sci.math.numanalysis polynomial division. post a messageon this topic post a message on a new topic 14 Jun 2000 Polynomial http://mathforum.org/epigone/sci.math.num-analysis/khangwhikhou

a topic from sci.math.num-analysis Polynomial Division post a message on this topic post a message on a new topic 14 Jun 2000 Polynomial Division , by Sinan Ozel 14 Jun 2000 Re: Polynomial Division , by Miguel A. Lerma 14 Jun 2000 Re: Polynomial Division , by patrick_powers@my-deja.com 17 Jun 2000 Re: Polynomial Division , by Russell Easterly 18 Jun 2000 Re: Polynomial Division , by Virgil 18 Jun 2000 Re: Polynomial Division , by David Wilkinson 7 Jul 2000 Re: Polynomial Division , by Rolie Baldock 7 Jul 2000 Re: Polynomial Division , by Lynn Killingbeck 8 Jul 2000 Re: Polynomial Division , by Rolie Baldock 8 Jul 2000 Re: Polynomial Division , by David Wilkinson 8 Aug 2001 Polynomial Division , by Ewen Miller 8 Aug 2001 Re: Polynomial Division , by David Wilkinson 9 Aug 2001 Re: Polynomial Division , by Ewen Miller 9 Aug 2001 Re: Polynomial Division , by Michel OLAGNON 9 Aug 2001 Re: Polynomial Division , by Lynn Killingbeck 13 Aug 2001 Re: Polynomial Division , by Ewen Miller 14 Aug 2001 Re: Polynomial Division , by Martin Brown 9 Aug 2001 Re: Polynomial Division , by Lynn Killingbeck 9 Aug 2001 Re: Polynomial Division , by David Wilkinson 9 Aug 2001 Re: Polynomial Division , by Carl DeVore The Math Forum

28. Improved Parallel Polynomial Division And Its Extensions - Bini Improved Parallel polynomial division and Its Extensions (1992) (MakeCorrections) (1 citation) Dario Bini Victor Pan September 1992. http://citeseer.ist.psu.edu/bini92improved.html

29. Citations Improved Parallel Polynomial Division And Its D. Bini and V. Pan. Improved parallel polynomial division and its extensions.Proc. Improved parallel polynomial division and its extensions. Proc. http://citeseer.ist.psu.edu/context/160380/341874

30. Long Polynomial Division 6x 2 + x 9 2x - 1. Set up the long division. 3x =, 6x 2 2x, . Notes. 6x 2 + x- 9 = (2x - 1)(3x + 2) - 7. Dividend, 6x 2 + x - 9. Divisor, 2x - 1. Quotient,3x + 2. http://www.sci.wsu.edu/~kentler/Fall97_101/Chapter5/lpd_2.html

Problem: Divide + x - 9 Set up the long division Choose since Subtract 6x - 3x from 6x + x - 9. Result is Choose since Subtract 4x - 2 from 4x - 9. Result is is the remainder. Answer: + x - 9 Notes + x - 9 = (2x - 1)(3x + 2) - 7 Dividend + x - 9 Divisor Quotient Remainder

31. Long Polynomial Division x 2 3. Set up the long division. Notice the 0 s put in as place holders for missingpowers of x. x 2 =, x 4 x 2, . Dividend, x 4 - 2x 3 + 8x - 14. Divisor, x 2 - 3. http://www.sci.wsu.edu/~kentler/Fall97_101/Chapter5/lpd_3.html

Problem: Divide x x Set up the long division. Notice the 's put in as place holders for missing powers of x. x x x Choose x since x matches x x = x (x Subtract x from x Result is x Choose since matches -2x = -2x(x Subtract -2x + 6x from Result is x Choose since matches 3x = 3(x Subtract 3x - 9 from Result is is the remainder. Answer: x x x x Notes x + 8x - 14 = (x - 3)(x Dividend x Divisor x Quotient x Remainder

32. Polynomial Division 1 ?( ?) ( polynomial division Version 1 ). ?( ?) ( polynomial division Version 2 ). http://lpl.hkcampus.net/~lpl-wwk/Casio50/Polynomial Division 1.htm

¦h¶µ¦¡°£ªk ( ²Ä¤@ª© ) ( Polynomial Division : Version 1 ) ¡A³Ì«á§ó·s¤é´Á 14 AUG 2003 ¡C) ( Quartic Polynomial ) ³Q¤@­Ó¤@¦¸¦h¶µ¦¡ ( Linear Polynomial ) °£©Ò±oªº°Ó¦¡ ( Quotient ) ¤Î¾l¼Æ ( Remainder ) ¡C 75 bytes ? ¡÷ A : ? ¡÷ B : ? ¡÷ C : ? ¡÷ D : ? ¡÷ X : ? ¡÷ Y : ? ¡÷ M : -M Y ¡÷ M : A Y ¡÷ A B Y + AM ¡÷ B C Y + BM ¡÷ C D Y + CM ¡÷ D X + DMY ¡÷ X MODE MODE MODE 2 ¨Ò¡G­pºâ ªº°Ó¦¡¤Î¾l¼Æ¡C Prog ¡A¦A«ö A? ¡A¦A«ö 2 EXE 3 EXE 5 EXE 4 EXE 6 EXE coefficient 2 EXE 1 EXE ( °£¦¡ªº«Y¼Æ ) x ªº«Y¼Æ ) ¦A«ö EXE x ªº«Y¼Æ ) ¦A«ö EXE x ªº«Y¼Æ ) ¦A«ö EXE ¦A«ö EXE ( ¾l¼Æ ) ¥ç§Y¬O»¡°Ó¦¡¬O x + x ¡A¾l¼Æ¬O ¡C RCL A ¡B RCL B ¡B RCL C RCL D RCL X ¦pªG³Q°£¦¡¬O¤T¦¸©Î§ó§C¦¸ªº¦h¶µ¦¡¡A¥u»Ý±N¬ÛÀ³ªº«Y¼Æ¿é¤J §Y¥i¡C ¦h¶µ¦¡­¼ªk ( ²Ä¤@ª© ) ( Polynomial Multiplication : Version 1 ) ¦h¶µ¦¡­¼ªk ( ²Ä¤Gª© ) ( Polynomial Multiplication : Version 2 ) ¦h¶µ¦¡°£ªk ( ²Ä¤Gª© ) ( Polynomial Division : Version 2 ) ¦h¶µ¦¡°£ªk ( ²Ä¤Tª© ) ( Polynomial Division : Version 3 )

33. Polynomial Division 3 ?( ?) ( polynomial division Version 3 ). ?( ?) ( polynomial division Version 1 ). http://lpl.hkcampus.net/~lpl-wwk/Casio50/Polynomial Division 3.htm

¦h¶µ¦¡°£ªk ( ²Ä¤Tª© ) ( Polynomial Division : Version 3 ) ¡A³Ì«á§ó·s¤é´Á 14 MAR 2004 ¡C) ( Polynomial ) ³Q¤@­Ó¤@¦¸¦h¶µ¦¡ ( Linear Polynomial ) °£©Ò±oªº°Ó¦¡ ( Quotient ) ¤Î¾l¼Æ ( Remainder ) ¡C 48 bytes Mem clear : ? ¡÷ A : ? ¡÷ B : ? ¡÷ D : Lbl 1 : ? ¡÷ X : X ¡V BC A ¡÷ C : C MODE MODE MODE 2 ¨Ò¡G­pºâ ªº°Ó¦¡¤Î¾l¼Æ¡C Prog ¡A¦A«ö A? ¡A¦A«ö 2 EXE 1 EXE ( °£¦¡ªº«Y¼Æ ) ¦A«ö 4 EXE ( ³Q°£¦¡ªº¦¸¼Æ degree ¡A§Y¬O³Q°£¦¡³Ì°ª¾­ªº¼Æ­È ) ¦A«ö 2 EXE ( ³Q°£¦¡ªº²Ä¤@­Ó«Y¼Æ¡A¦¹®É¬O x ªº«Y¼Æ )¡Aà ã¥Ü ( °Ó¦¡ªº²Ä¤@­Ó«Y¼Æ¡A¦¹®É¬O x ªº«Y¼Æ ) ¦A«ö 3 EXE ( ³Q°£¦¡ªº²Ä¤G­Ó«Y¼Æ¡A¦¹®É¬O x ªº«Y¼Æ )¡Aà ã¥Ü ( °Ó¦¡ªº²Ä¤G­Ó«Y¼Æ¡A¦¹®É¬O x ªº«Y¼Æ ) ¦A«ö 5 EXE ( ³Q°£¦¡ªº²Ä¤T­Ó«Y¼Æ¡A¦¹®É¬O x ªº«Y¼Æ )¡Aà ã¥Ü ( °Ó¦¡ªº²Ä¤T­Ó«Y¼Æ¡A¦¹®É¬O x ªº«Y¼Æ ) ¦A«ö 4 EXE x ªº«Y¼Æ )¡Aà ã¥Ü ¦A«ö 6 EXE ( ³Q°£¦¡ªº³Ì«á¤@­Ó«Y¼Æ¡A±`¼Æ¶µ )¡Aà ã¥Ü ( ¾l¼Æ ) ¥ç§Y¬O»¡°Ó¦¡¬O x + x ¡A¾l¼Æ¬O ¡C ¦h¶µ¦¡­¼ªk ( ²Ä¤@ª© ) ( Polynomial Multiplication : Version 1 ) ¦h¶µ¦¡­¼ªk ( ²Ä¤Gª© ) ( Polynomial Multiplication : Version 2 ) ¦h¶µ¦¡°£ªk ( ²Ä¤@ª© ) ( Polynomial Division : Version 1 ) ¦h¶µ¦¡°£ªk ( ²Ä¤Gª© ) ( Polynomial Division : Version 2 )

34. Polynomial Division And Zeros Of A Polynomial polynomial division and Zeros of a Polynomial. Lecture Notesprovided by Sharon Walker last update 6/23/99 sw. http://fym.la.asu.edu/~fym/mat117_online/lessons/ch4/4_4/poly_division_zeros.htm

Polynomial Division and Zeros of a Polynomial Lecture Notes provided by Sharon Walker - last update: 6/23/99 sw

35. Module 1 -- Polynomial Division Instructional Unit Polynomial and Rational Functions. DayOne. by. Behnaz Rouhani. Return to Behnaz Rouhani s Page http://jwilson.coe.uga.edu/EMT668/EMAT6680.2002/Rouhani/IU/module1.html

Instructional Unit Polynomial and Rational Functions Day One by Behnaz Rouhani Return to Behnaz Rouhani's Page

36. Left Or Right Polynomial Division Left or right polynomial division. The operator nc_divide computesthe one sided quotient and remainder of two polynomials nc_divide http://www.uni-koeln.de/REDUCE/ncpoly/section3_5.html

Next: Left or right polynomial reduction Up: NCPOLY: Computation in non-commutative polynomial ideals Previous: Left or right polynomial division The operator computes the one sided quotient and remainder of two polynomials: The result is a list with quotient and remainder. The division is performed as a pseudo-division, multiplying by coefficients if necessary. The result is defined by the relation for direction and for direction where is an expression that does not contain any of the ideal variables, and the leading term of is lower than the leading term of according to the actual term order. Next: Left or right polynomial reduction Up: NCPOLY: Computation in non-commutative polynomial ideals Previous: Strotmann@RRz.Uni-Koeln.DE Tue Jan 17 15:55:59 MET 1995 see also: REDUCE Home Page

37. 5 Left Or Right Polynomial Division 5 Left or right polynomial division. The operator nc_divide computesthe one sided quotient and remainder of two polynomials nc_divide http://www.uni-koeln.de/REDUCE/3.6/doc/ncpoly/node5.html

TOP Next: 6 Left or right polynomial reduction Up: NCPOLY: Computation in noncommutative polynomial ideals Previous: Top: REDUCE Online Documentation 5 Left or right polynomial division The operator computes the one sided quotient and remainder of two polynomials: The result is a list with quotient and remainder. The division is performed as a pseudodivision, multiplying by coefficients if necessary. The result is defined by the relation for direction left and for direction right where is an expression that does not contain any of the ideal variables, and the leading term of is lower than the leading term of according to the actual term order. TOP Next: 6 Left or right polynomial reduction Up: NCPOLY: Computation in noncommutative polynomial ideals Previous: Top: REDUCE Online Documentation REDUCE WWW Pages maintained by Strotmann@RRz.Uni-Koeln.DE at

38. CenterSpace API Documentation - Polynomial Division Operator NMath Core Reference Guide, Version 2.1. polynomial division Operator.Divides a polynomial by a scalar. public static Polynomial operator http://www.centerspace.net/doc/NMath/Core/ref/CenterSpace.NMath.Core.Polynomial.

NMath Core Reference Guide Version 2.1 Polynomial Division Operator  Divides a polynomial by a scalar. public static  Polynomial  operator /( Polynomial p double s Parameters p A polynomial. s A scalar. Return Value A new polynomial containing the quotient. See Also Polynomial Class Polynomial Members CenterSpace.NMath.Core Namespace

39. Real Roots Of Polynomial Functions Again, consider our basic definition of polynomial division Dividend f(x). Divisorh(x). This we will call the remainder theorem for polynomial division. http://id.mind.net/~zona/mmts/functionInstitute/polynomialFunctions/roots/realRo

Real Roots of Polynomial Functions Roots Polynomial Functions Function Institute Contents ... Home Definition of terms and symbols when dividing polynomials: Dividend: f(x) Divisor: h(x) Quotient: q(x) Remainder: r(x) If any of these are constants, for example if r(x) is constant, as in: r(x) = 5 or: r(x) = a then variable, rather than function, notation may be used for that value, as in: r = 5 or: r = a When f(x) is divided by h(x), the result is the value of q(x) plus r(x), as in: f(x)/h(x) = q(x) + r(x) This can also be written as: f(x) = h(x)q(x) + r(x) The remainder, r(x), will either be equal to 0, or it will be less in degree than the degree of the divisor, h(x). If h(x) has a degree of 1, then the degree of the remainder must be 0. That is, the remainder must be a constant, as in: r(x) = cx = c Under these conditions variable notation is fine, as in: r = c Therefore, if f(x) is divided by the linear polynomial (x - c), the remainder is a constant, r. Again, consider our basic definition of polynomial division: Dividend: f(x) Divisor: h(x) Quotient: q(x) Remainder: r(x) f(x) = h(x)q(x) + r(x) Make the divisor, h(x), equal to the zero degree polynomial (x - c). This will create a remainder, r, that is a constant.

40. Synthetic Division with division? Consider dividing f(x) = 4x 3 3x 2 + x - 4 by (x- 2). Standard polynomial division would look like this 4x 2 http://id.mind.net/~zona/mmts/functionInstitute/polynomialFunctions/roots/synthe

Synthetic Division Polynomial Functions Function Institute Contents Index ... Home Consider this polynomial function: f(x) = 4x + x - 4 Suppose that we evaluate it at an input of x = 2, like this: f(2) = 4(2 f(2) = 32 - 12 = 2 - 4 f(2) = 18 In this process we raised the input to a power, as in 2 Let us see that there is a way to evaluate this polynomial function using only multiplication and addition. Start with the original polynomial and factor out an x. So, this: + x - 4 Becomes: x(4x Factor out another x from the parenthesized expression: x(x(4x - 3) + 1) - 4 Now, imagine that you evaluate f(x) at x = 2. Begin with the inner most expression. Place a 2 for the input value of x, as in: x(x(4(2) - 3) + 1) - 4 Now you would multiply 2 (the input) by 4 (the original coefficient of x ) and then add -3 (the original coefficient of x ). This would evaluate to 5. The expression now looks like: x(x(5) + 1) - 4 Place a 2 for the next input value of x, as in: x(2(5) + 1) - 4 Now you would multiply 2 (the input) by 5 and then add 1 (the original coefficient of x). This would evaluate to 11. The expression now looks like: x(11) - 4 Place a 2 for the last input value of x, as in:

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

Page 2     21-40 of 91    Back | 1  | 2  | 3  | 4  | 5  | Next 20