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<para>This module is from<link document="col10614">Elementary Algebra</link>by Denny Burzynski and Wade Ellis, Jr.</para><para>A detailed study of arithmetic operations with rational expressions is presented in this chapter, beginning with the definition of a rational expression and then proceeding immediately to a discussion of the domain. The process of reducing a rational expression and illustrations of multiplying, dividing, adding, and subtracting rational expressions are also included. Since the operations of addition and subtraction can cause the most difficulty, they are given particular attention. We have tried to make the written explanation of the examples clearer by using a "freeze frame" approach, which walks the student through the operation step by step.</para><para>The five-step method of solving applied problems is included in this chapter to show the problem-solving approach to number problems, work problems, and geometry problems. The chapter also illustrates simplification of complex rational expressions, using the combine-divide method and the LCD-multiply-divide method.</para><para>Objectives of this module: be able to divide a polynomial by a monomial, understand the process and be able to divide a polynomial by a polynomial.</para>


  • Dividing a Polynomial by a Monomial
  • The Process of Division
  • Review of Subtraction of Polynomials
  • Dividing a Polynomial by a Polynomial

Dividing a polynomial by a monomial

The following examples illustrate how to divide a polynomial by a monomial. The division process is quite simple and is based on addition of rational expressions.

a c + b c = a + b c

Turning this equation around we get

a + b c = a c + b c

Now we simply divide c into a , and c into b . This should suggest a rule.

Dividing a polynomial by a monomial

To divide a polynomial by a monomial, divide every term of the polynomial by the monomial.

Sample set a

3 x 2 + x 11 x . Divide every term of   3 x 2   +   x 11   by   x . 3 x 2 x + x x 11 x = 3 x + 1 11 x

8 a 3 + 4 a 2 16 a + 9 2 a 2 . Divide every term of   8 a 3   +   4 a 2 16 a   + 9   by   2 a 2 . 8 a 3 2 a 2 + 4 a 2 2 a 2 16 a 2 a 2 + 9 2 a 2 = 4 a + 2 8 a + 9 2 a 2

4 b 6 9 b 4 2 b + 5 4 b 2 . Divide every term of 4 b 6 9 b 4 2 b + 5 by 4 b 2 . 4 b 6 4 b 2 9 b 4 4 b 2 2 b 4 b 2 + 5 4 b 2 = b 4 + 9 4 b 2 + 1 2 b 5 4 b 2

Practice set a

Perform the following divisions.

2 x 2 + x 1 x

2 x + 1 1 x

3 x 3 + 4 x 2 + 10 x 4 x 2

3 x + 4 + 10 x 4 x 2

a 2 b + 3 a b 2 + 2 b a b

a + 3 b + 2 a

14 x 2 y 2 7 x y 7 x y

2 x y 1

10 m 3 n 2 + 15 m 2 n 3 20 m n 5 m

2 m 2 n 2 3 m n 3 + 4 n

The process of division

In Section [link] we studied the method of reducing rational expressions. For example, we observed how to reduce an expression such as

x 2 2 x 8 x 2 3 x 4

Our method was to factor both the numerator and denominator, then divide out common factors.

( x 4 ) ( x + 2 ) ( x 4 ) ( x + 1 )

( x 4 ) ( x + 2 ) ( x 4 ) ( x + 1 )

x + 2 x + 1

When the numerator and denominator have no factors in common, the division may still occur, but the process is a little more involved than merely factoring. The method of dividing one polynomial by another is much the same as that of dividing one number by another. First, we’ll review the steps in dividing numbers.

  1. 35 8 .  We are to divide 35 by 8.
  2. Long division showing eight dividing thirty five. This division is not performed completely.   We try 4, since 32 divided by 8 is 4.
  3. Long division showing eight dividing thirty five, with four at quotient's place. This division is not performed completely. Multiply 4 and 8.
  4. Long division showing eight dividing thirty five, with four at quotient's place. Thirty two is written under thirty five. This division is not performed completely Subtract 32 from 35.
  5. Long division showing eight dividing thirty five, with four at quotient's place. Thirty two is written under thirty five and three is written as the subtraction of thirty five and thirty two. Since the remainder 3 is less than the divisor 8, we are done with the 32 division.
  6. 4 3 8 .   The quotient is expressed as a mixed number.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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