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5 x 3 ( y 7 ) means there are five x 3 ( y 7 ) ' s . It could also mean there are 5 x 3 ( x 7 ) ' s . It could also mean there are 5 ( x 7 ) x 3 ' s .

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Practice set d

What does the coefficient of a quantity tell us?

The difference between coefficients and exponents

It is important to keep in mind the difference between coefficients and exponents .

Coefficients record the number of like terms in an algebraic expression.
x + x + x + x 4 terms = 4 x coefficient is 4
Exponents record the number of like factors in a term.
x x x x 4 factors = x 4 exponent is 4

In a term, the coefficient of a particular group of factors is the remaining group of factors.

how many of that quantity there are

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Sample set e

3 x .

The coefficient of x is 3.

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6 a 3 .

The coefficient of a 3 is 6.

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9 ( 4 a ) .

The coefficient of ( 4 a ) is 9.

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3 8 x y 4 .

The coefficient of x y 4 is 3 8 .

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3 x 2 y .

The coefficient of x 2 y is 3; the coefficient of y is 3 x 2 ; and the coefficient of 3 is x 2 y .

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4 ( x + y ) 2 .

The coefficient of ( x + y ) 2 is 4; the coefficient of 4 is ( x + y ) 2 ; and the coefficient of ( x + y ) is 4 ( x + y ) since 4 ( x + y ) 2 can be written as 4 ( x + y ) ( x + y ) .

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Practice set e

Determine the coefficients.
In the term 6 x 3 , the coefficient of
(a) x 3 is .
(b) 6 is .

(a) 6 (b) x 3

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In the term 3 x ( y 1 ) , the coefficient of
(a) x ( y 1 ) is .
(b) ( y 1 ) is .
(c) 3 ( y 1 ) is .
(d) x is .
(e) 3 is .
(f) The numerical coefficient is .

(a) 3 (b) 3 x (c) x (d) 3 ( y 1 ) (e) x ( y 1 ) (f) 3

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In the term 10 a b 4 , the coefficient of
(a) a b 4 is .
(b) b 4 is .
(c) a is .
(d) 10 is .
(e) 10 a b 3 is .

(a) 10 (b) 10 a (c) 10 b 4 (d) a b 4 (e) b

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Exercises

What is an algebraic expression?

An algebraic expression is a number, a letter, or a collection of numbers and letters along with meaningful signs of operation.

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Why is the number 14 considered to be an expression?

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Why is the number x considered to be an expression?

x is an expression because it is a letter (see the definition).

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For the expressions in the following problems, write the number of terms that appear and then list the terms.

6 x 10

two : 6 x , 10

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5 x 2 + 6 x 2

three : 5 x 2 , 6 x , 2

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5 c z

one : 5 c z

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4 y 3

one : 4 y 3

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a + 1

two : a , 1

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2 x + x + 7

three : 2 x , x , 7

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( a + 1 ) + ( a 1 )

two : ( a + b ) , ( a 1 )

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For the following problems, list, if any should appear, the common factors in the expressions.

x 2 + 5 x 2 2 x 2

x 2

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2 ( a + b ) 3 ( a + b )

( a + b )

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8 a 2 ( b + 1 ) 10 a 2 ( b + 1 )

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14 a b 2 c 2 ( c + 8 ) + 12 a b 2 c 2

2 a b 2 c 2

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9 a ( a 3 ) 2 + 10 b ( a 3 )

( a 3 )

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12 a 3 b 2 c 7 ( b + 1 ) ( c a )

no commom factors

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5.2 ( a + 7 ) 2 + 17.1 ( a + 7 )

( a + 7 )

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3 4 x 2 y 2 z 2 + 3 8 x 2 z 2

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9 16 ( a 2 b 2 ) + 9 32 ( b 2 a 2 )

9 32

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For the following problems, note how many:

z ' s in 12 z ?

12

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x 2 's in 5 x 2 ?

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y 3 's in 6 y 3 ?

6

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x y ' s in 9 x y ?

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a 2 b ' s in 10 a 2 b ?

10

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( a + 1 ) ' s in 4 ( a + 1 ) ?

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( 9 + y ) ' s in 8 ( 9 + y ) ?

8

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y 2 's in 3 x 3 y 2 ?

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12 x ' s in 12 x 2 y 5 ?

x y 5

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( a + 5 ) ' s in 2 ( a + 5 ) ?

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( x y ) ' s in 5 x ( x y ) ?

5 x

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( x + 1 ) ' s in 8 ( x + 1 ) ?

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2 ' s in 2 x 2 ( x 7 ) ?

x 2 ( x 7 )

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3 ( a + 8 ) ' s in 6 x 2 ( a + 8 ) 3 ( a 8 ) ?

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For the following problems, a term will be given followed by a group of its factors. List the coefficient of the given group of factors.

12 a 2 b 3 c 2 r 7 ; a 2 c 2 r 7

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6 x 2 b 2 ( c 1 ) ; c 1

6 x 2 b 2

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10 x ( x + 7 ) 2 ; 10 ( x + 7 )

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9 a 2 b 5 ; 3 a b 3

3 a b 2

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15 x 4 y 4 ( z + 9 a ) 3 ; ( z + 9 a )

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( 4 ) a 6 b 2 ; a b

( 4 ) a 5 b

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( 11 a ) ( a + 8 ) 3 ( a 1 ) ; ( a + 8 ) 2

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Exercises for review

( [link] ) Simplify [ 2 x 8 ( x 1 ) 5 x 4 ( x 1 ) 2 ] 4 .

16 x 16 ( x 1 ) 12

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( [link] ) Supply the missing phrase. Absolute value speaks to the question of and not "which way."

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( [link] ) Find the value of [ 6 ( 4 2 ) + 7 ( 3 + 5 ) ] .

50

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( [link] ) Find the value of 2 5 4 2 3 2 .

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( [link] ) Express 0.0000152 using scientific notation.

1.52 × 10 5

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Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
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John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
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Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
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Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
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fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir 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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