1. Polynomial Division And Factoring That is, we will begin by demonstrating how to divide polynomials. polynomial division is very similar to ordinary integer division. http://campus.northpark.edu/math/PreCalculus/Algebraic/Polynomial/Factoring/

Section 6.3: Polynomial Division and Factoring In the previous section , we discussed a technique for sketching polynomials that depended on our ability to find all the factors/roots of a polynomial. This is a very difficult problem, in general, and it is complicated by the fact that the answer depends on the number system you use: rational real , or complex numbers. Using the complex numbers is very convenient, because every polynomial factors completely into complex linear factors; unfortunately, actually finding all the factors is quite challenging. On the other extreme, using only rational numbers, we have a straightforward and moderately efficient technique for finding all possible linear factors. That is because, we can quickly convert the problem to that of factoring over the integers However , not all integer rational polynomials factor completely into linear factors. Working over the real numbers is somewhere in between these two extremes. Although we cannot give explain all these difficult issues in detail (that would take several more courses in advanced mathematics!), we can discuss some specific, elementary ideas and techniques that can be quite useful in certain cases. Specifically, we will discuss:

2. Dividing Polynomials Lesson - I Demonstrates how to do simple polynomial division/reduction problems. First of two in a series http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. Polynomial Division And Factoring: Practice Exercises Here are various Exercises to accompany the section polynomial division and Factoring. polynomial division. Use polynomial longdivision to compute the http://campus.northpark.edu/math/PreCalculus/Algebraic/Polynomial/Factoring/Exer

Polynomial Division and Factoring: Practice Exercises Here are various Exercises to accompany the section Polynomial Division and Factoring Polynomial Division Use polynomial long-division to compute the quotient, q , and remainder, r , after dividing p by d for each of the following pairs of polynomials. Check your answer by plugging your answers into the equation p d q r and simplifying. Divide p x x x x - 9 by d x x Divide p x x x x + 1 by d x x x Divide p x x x - 9 by d x x Pick your own polynomial, p , and a lower degree polynomial, d , and divide d into p to find the quotient, q , and remainder, r Repeat this Exercise as often as necessary until you are confident in your ability to divide polynomials Solution Likely Factors of Rational Polynomials and Rational Roots Use the Rational Root Theorem to list all possible rational roots and corresponding integral, linear factors of the following polynomials. x x x x x x Solution Use our strategy for factoring rational polynomials to factor each of the following polynomials as much as possible (i.e., find as many rational roots as possible). To help you narrow your search, some values of each polynomial are already given. Factor p x x x x Hint x p x Factor q x x x x Hint x p x Factor r x x x x x Hint x p x Solution Factoring Over the Real and Complex Numbers and Prime Polynomials For each of the following polynomials, factor them as much as possible over each of the following number systems:

4. Synthetic Division Lesson - I Explains the basic process of synthetic division, and compares synthetic division to long (polynomial) division. First of two in a series http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. Synthetic Division Lesson - I Synthetic division is a shorthand, or shortcut, method of polynomial To convert the polynomial division into the required mixed number format, http://www.purplemath.com/modules/synthdiv.htm

Purplemath — Your Algebra Resource This lesson may be printed out for personal use. Terms of (web)Use Synthetic Division - I Lessons Home Lesson pages: Synthetic division process, Factors and zeroes Synthetic division process Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor (and only works in this case). It is generally used, however, not for dividing out factors but for finding zeroes (or roots) of polynomials. If you are given, say, y x , you can factor this as y x x Then you can find the zeroes of y by setting each factor equal to zero and solving. You will find that x and x are the two zeroes of y You can, however, also work backwards from the zeroes to find the originating polynomial. For instance, if you are given that x and x are zeroes of a quadratic, then you know that

6. Polynomial Long Division Polynomial Long Division http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. Dividing Polynomials Lesson - I Demonstrates how to do simple polynomial division/reduction problems. First of two in a series http://www.purplemath.com/modules/polydiv.htm

Purplemath — Your Algebra Resource This lesson may be printed out for personal use. Terms of (web)Use Dividing Polynomials - I Lessons Home Lesson pages: Simplification and reduction, Polynomial long division Simplification and reduction There are two cases for dividing polynomials: either the "division" is really just simplification and reduction of a fraction, or else you need to do long division. Simplify This is just a simplification problem, because there is only one term in the polynomial you're dividing by. And, in this case, there is a common factor in the numerator (top) and denominator (bottom), so it's easy to reduce this fraction. There are two ways of proceeding. I can split the division into two fractions, each with only one term on top, and then reduce: ...or I can factor out the common factor from the top and bottom, and then cancel off: Either way, the answer is the same:

8. Long Division Of Polynomials two polynomials, and we want to divide one polynomial by another. One method is long division, a process similar to long division of two http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. Polynomial Division - Mathcentre mathcentre has been established to deliver mathematics support materials, free of charge, to both university professionals and students. http://www.mathcentre.ac.uk/resources.php/305

Polynomial Division Students Staff Search News ... Contact Us more information About Us Contact Us The mathcentre Team News ... Mailing List options open in a new window information link: Polynomial Division rating 5 out of 5 rated by 6 users Rate this resource PLEASE NOTE: These videos require Windows Media Player 10 or above. This resource is being hosted by the University of Portsmouth on their streaming-media server

10. Long Polynomial Division Problem Divide 6x2 + x 9 2x - 1. Set up the long division 3x = 6x2 2x . Choose 3x since 3x 2x matches 6x2. 6x2 - 3x = http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Resources For All Subjects - Algebra - Simplifying Algebraic Fractions Inc Polyn Algebra Simplifying algebraic fractions inc polynomial division polynomial division is a process used to simplify certain sorts of algebraic fraction. http://www.mathcentre.ac.uk/students.php/all_subjects/algebra/simplifying/resour

Students All Subjects Students Staff Search News ... Contact Us All Subjects Algebra Arithmetic Complex Numbers Differentiation ... Vectors Algebra - Simplifying algebraic fractions inc polynomial division Please select a resource from the list below. Quick Reference Simplifying fractions Fractions involving symbols occur frequently. It is necessary to be able to simplify these and rewrite them in different, but equivalent forms. In this leaflet, we revise how these processes are carried out. Teach Yourself Polynomial division Polynomial division is a process used to simplify certain sorts of algebraic fraction. It is very similar to long division of numbers. This booklet describes how the process is carried out. Simplifying Fractions This booklet explains how an algebraic fraction can be expressed in its lowest terms, or simplest form. Algebra Refresher A refresher booklet on Algebra Cwrs Gloywi Algebra An Algebra Refresher. This booklet revises basic algebraic techniques. This is a welsh language version. Test Yourself Diagnostic Test - Cubics Diagnostic test for cubic equations.

12. Long Polynomial Division Problem Divide x4 2x3 + 8x - 14 x2 - 3. Set up the long division. Notice the 0's put in as place holders for missing powers of x. x2 http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. Real Roots Of Polynomial Functions Again, consider our basic definition of polynomial division. Dividend f(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.

14. Http//math.usask.ca/readin/factor.html http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

15. Polynomial Division How do we divide the following polynomials? (x3 + x2 x + 2) / (x + 2). Hi Efrat,. Set it up as you would to divide integers. http://mathcentral.uregina.ca/QQ/database/QQ.09.03/efrat1.html

Quandaries and Queries How do we divide the following polynomials? (x + x - x + 2) / (x + 2) Hi Efrat, Set it up as you would to divide integers. x times x is x , hence the quotient starts with x . Multiplt x + 2 by x to get Subtract and bring down the -x. Can you see what to do next? Penny Go to Math Central

16. Division Of Polynomials II http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

17. Library.wolfram.com/webMathematica/Education/LongD Mathematics Weblog polynomial divisionpolynomial division Articles Steve - steve@sixthform.info @ 250pm students used to learn how to do polynomial long division before they were 16. http://library.wolfram.com/webMathematica/Education/LongDivide.jsp

18. Fast Configurable Polynomial Division For Error Control Coding July 09 11, 2001. Taormina, Italy p. 0158 Fast Configurable polynomial division for Error Control Coding Applications http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

19. Polynomial Division polynomial division Posted by Steve on 19.06.2005 @ 145050 in Articles A long time ago UK students used to learn how to do polynomial long division before http://sixthform.info/maths/b2print.php?p=84

20. DBforums - Polynomial Division In C polynomial division in C. I want to make a two polynom division in C. I wonder if there is any library that includes such a function. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

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