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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

the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza Reply
what is cell divisoin?
Aron Reply
Diversity of living thing
ISCONT
what is cell division
Aron Reply
Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
AI-Robot
What is life?
Allison Reply
life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
Mohamed
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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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