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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

explain and give four Example hyperbolic function
Lukman Reply
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
SABAL Reply
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
ok
Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
mariel Reply
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
Harshika Reply
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Shirley Reply
please can go further on polynomials quadratic
Abdullahi
hi mam
Mark
I need quadratic equation link to Alpa Beta
Abdullahi Reply
find the value of 2x=32
Felix Reply
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
yes i wantt to review
Mark
use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
how do we prove the quadratic formular
Seidu Reply
please help me prove quadratic formula
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
Shirley Reply
thank you help me with how to prove the quadratic equation
Seidu
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris 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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