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Sample set b

Identify the factors in each term.

9 a 2 6 a 12 contains three terms. Some of the factors in each term are

first term: 9 and a 2 , or , 9 and a and a second term: 6 and a third term: 12 and 1 , or , 12 and 1

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14 x 5 y + ( a + 3 ) 2 contains two terms. Some of the factors of these terms are

first term: 14 , x 5 , y second term: ( a + 3 ) and ( a + 3 )

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Practice set b

In the expression 8 x 2 5 x + 6 , list the factors of the
first term:
second term:
third term:

8, x , x ; 5 , x ; 6 and 1 or 3 and 2

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In the expression 10 + 2 ( b + 6 ) ( b 18 ) 2 , list the factors of the
first term:
second term:

10 and 1 or 5 and 2; 2, b + 6 , b 18 , b 18

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Common factors

Common factors

Sometimes, when we observe an expression carefully, we will notice that some particular factor appears in every term. When we observe this, we say we are observing common factors . We use the phrase common factors since the particular factor we observe is common to all the terms in the expression. The factor appears in each and every term in the expression.

Sample set c

Name the common factors in each expression.

5 x 3 7 x 3 + 14 x 3 .

The factor x 3 appears in each and every term. The expression x 3 is a common factor.

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4 x 2 + 7 x .

The factor x appears in each term. The term 4 x 2 is actually 4 x x . Thus, x is a common factor.

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12 x y 2 9 x y + 15 .

The only factor common to all three terms is the number 3. (Notice that 12 = 3 4 , 9 = 3 3 , 15 = 3 5 .)

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3 ( x + 5 ) 8 ( x + 5 ) .

The factor ( x + 5 ) appears in each term. So, ( x + 5 ) is a common factor.

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45 x 3 ( x 7 ) 2 + 15 x 2 ( x 7 ) 20 x 2 ( x 7 ) 5 .

The number 5, the x 2 , and the ( x 7 ) appear in each term. Also, 5 x 2 ( x 7 ) is a factor (since each of the individual quantities is joined by a multiplication sign). Thus, 5 x 2 ( x 7 ) is a common factor.

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10 x 2 + 9 x 4 .

There is no factor that appears in each and every term. Hence, there are no common factors in this expression.

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Practice set c

List, if any appear, the common factors in the following expressions.

x 2 + 5 x 2 9 x 2

x 2

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4 x 2 8 x 3 + 16 x 4 24 x 5

4 x 2

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4 ( a + 1 ) 3 + 10 ( a + 1 )

2 ( a + 1 )

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9 a b ( a 8 ) 15 a ( a 8 ) 2

3 a ( a 8 )

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14 a 2 b 2 c ( c 7 ) ( 2 c + 5 ) + 28 c ( 2 c + 5 )

14 c ( 2 c + 5 )

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6 ( x 2 y 2 ) + 19 x ( x 2 + y 2 )

no common factor

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Coefficients

Coefficient

In algebra, as we now know, a letter is often used to represent some quantity. Suppose we represent some quantity by the letter x . The notation 5 x means x + x + x + x + x . We can now see that we have five of these quantities. In the expression 5 x , the number 5 is called the numerical coefficient of the quantity x . Often, the numerical coefficient is just called the coefficient. The coefficient of a quantity records how many of that quantity there are.

Sample set d

12 x means there are 12 x ' s .

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4 a b means there are four a b ' s .

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10 ( x 3 ) means there are ten ( x 3 ) ' s .

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1 y means there is one y . We usually write just y rather than 1 y since it is clear just by looking that there is only one y .

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7 a 3 means there are seven a 3 ' s .

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5 a x means there are five a x ' s . It could also mean there are 5 a x ' s . This example shows us that it is important for us to be very clear as to which quantity we are working with. When we see the expression 5 a x we must ask ourselves "Are we working with the quantity a x or the quantity x ?".

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6 x 2 y 9 means there are six x 2 y 9 ' s . It could also mean there are 6 x 2 y 9 ' s . It could even mean there are 6 y 9 x 2 ' s .

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Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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