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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. Factoring is an essential skill for success in algebra and higher level mathematics courses. Therefore, we have taken great care in developing the student's understanding of the factorization process. The technique is consistently illustrated by displaying an empty set of parentheses and describing the thought process used to discover the terms that are to be placed inside the parentheses.The factoring scheme for special products is presented with both verbal and symbolic descriptions, since not all students can interpret symbolic descriptions alone. Two techniques, the standard "trial and error" method, and the "collect and discard" method (a method similar to the "ac" method), are presented for factoring trinomials with leading coefficients different from 1. This module contains the exercise supplement for the chapter "Factoring Polynomials".

Exercise supplement

Finding the factors of a monomial ( [link] )

For the following problems, the first quantity represents the product and the second quantity represents a factor. Find the other factor.

44 a 2 b 2 c , 11 b 2

4 a 2 c

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50 m 3 n 5 p 4 q , 10 m 3 q

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51 ( a + 1 ) 2 ( b + 3 ) 4 , 3 ( a + 1 )

17 ( a + 1 ) ( b + 3 ) 4

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26 ( x + 2 y ) 3 ( x y ) 2 , 13 ( x y )

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8 x 5 y 4 ( x + y ) 4 ( x + 3 y ) 3 , 2 x ( x + y ) ( x + 3 y )

4 x 4 y 4 ( x + y ) 3 ( x + 3 y ) 2

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( 6 a 5 b ) 10 ( 7 a b ) 8 ( a + 3 b ) 7 , ( 6 a 5 b ) 7 ( 7 a b ) 7 ( a + 3 b ) 7

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12 x n + 6 y 2 n 5 , 3 x n + 1 y n + 3

4 x 5 y n 8

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400 a 3 n + 10 b n 6 c 4 n + 7 , 20 a 2 n + 8 c 2 n 1

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16 x 32 , 16

( x 2 )

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24 a 2 6 a , 6 a

4 a 1

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88 x 4 33 x 3 + 44 x 2 + 55 x , 11 x

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9 y 3 27 y 2 + 36 y , 3 y

3 y 2 + 9 y 12

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4 m 6 16 m 4 + 16 m 2 , 4 m

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5 x 4 y 3 + 10 x 3 y 2 15 x 2 y 2 , 5 x 2 y 2

x 2 y 2 x + 3

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21 a 5 b 6 c 4 ( a + 2 ) 3 + 35 a 5 b c 5 ( a + 2 ) 4 , 7 a 4 b ( a + 2 ) 2

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x 2 y c 2 , 1

x + 2 y + c 2

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Factoring a monomial from a polynomial ( [link] ) - the greatest common factor ( [link] )

For the following problems, factor the polynomials.

3 y 2 + 27 y

3 y ( y + 9 )

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21 ( x + 5 ) + 9

3 ( 7 x + 38 )

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m a 3 m

m ( a 3 1 )

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r 2 ( r + 1 ) 3 3 r ( r + 1 ) 2 + r + 1

( r + 1 ) [ r 2 ( r + 1 ) 2 3 r ( r + 1 ) + 1 ]

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( 10 - 3 x ) ( 2 + x ) + 3 ( 10 3 x ) ( 7 + x )

( 10 3 x ) ( 23 + 4 x )

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Factoring by grouping ( [link] )

For the following problems, use the grouping method to factor the polynomials. Some may not be factorable.

x y + 4 x 3 y 12

( x 3 ) ( y + 4 )

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2 a b 8 b 3 a b 12 a

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a 2 7 a + a b 7 b

( a + b ) ( a 7 )

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r 2 + r s r s

( r 1 ) ( r + s )

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8 a 2 b c + 20 a 2 b c + 10 a 3 b 3 c + 25 a 3 b 3

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a ( a + 6 ) ( a + 6 ) + a ( a 4 ) ( a 4 )

2 ( a + 1 ) ( a 1 )

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a ( 2 x + 7 ) 4 ( 2 x + 7 ) + a ( x 10 ) 4 ( x 10 )

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Factoring two special products ( [link] ) - factoring trinomials with leading coefficient other than 1 ( [link] )

For the following problems, factor the polynomials, if possible.

m 2 36

( m + 6 ) ( m 6 )

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a 2 + 8 a + 16

( a + 4 ) 2

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m 2 + m + 1

not factorable

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a 2 + 9 a + 20

( a + 5 ) ( a + 4 )

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x 2 + 14 x + 40

( x + 10 ) ( x + 4 )

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n 2 14 n + 49

( n 7 ) 2

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a 2 9 a + 20

( a 5 ) ( a 4 )

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4 a 2 9 a 9

( 4 a + 3 ) ( a 3 )

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42 a 2 + 5 a 2

( 6 a 1 ) ( 7 a + 2 )

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56 m 2 + 26 m + 6

2 ( 28 m 2 + 13 m + 3 )

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4 x 2 + 4 x y 3 y 2

( 2 x + 3 y ) ( 2 x y )

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2 x 2 + 6 x 20

2 ( x 2 ) ( x + 5 )

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x 3 + 3 x 2 4 x

x ( x + 4 ) ( x 1 )

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3 y 4 27 y 3 + 24 y 2

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15 a 2 b 2 a b 2 b

b ( 15 a 2 b a 2 )

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18 a 2 6 a + 1 2

( 6 a 1 ) ( 3 a 1 2 )

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4 x 2 12 x y + 9 y 2

( 2 x 3 y ) 2

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r 6 s 8 + 6 r 3 s 4 p 2 q 6 + 9 p 4 q 12

( r 3 s 4 + 3 p 2 q 6 ) 2

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a 4 2 a 2 b 15 b 2

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81 a 8 b 12 c 10 25 x 20 y 18

( 9 a 4 b 6 c 5 + 5 x 10 y 9 ) ( 9 a 4 b 6 c 5 5 x 10 y 9 )

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Questions & Answers

if three forces F1.f2 .f3 act at a point on a Cartesian plane in the daigram .....so if the question says write down the x and y components ..... I really don't understand
Syamthanda Reply
hey , can you please explain oxidation reaction & redox ?
Boitumelo Reply
hey , can you please explain oxidation reaction and redox ?
Boitumelo
for grade 12 or grade 11?
Sibulele
the value of V1 and V2
Tumelo Reply
advantages of electrons in a circuit
Rethabile Reply
we're do you find electromagnetism past papers
Ntombifuthi
what a normal force
Tholulwazi Reply
it is the force or component of the force that the surface exert on an object incontact with it and which acts perpendicular to the surface
Sihle
what is physics?
Petrus Reply
what is the half reaction of Potassium and chlorine
Anna Reply
how to calculate coefficient of static friction
Lisa Reply
how to calculate static friction
Lisa
How to calculate a current
Tumelo
how to calculate the magnitude of horizontal component of the applied force
Mogano
How to calculate force
Monambi
a structure of a thermocouple used to measure inner temperature
Anna Reply
a fixed gas of a mass is held at standard pressure temperature of 15 degrees Celsius .Calculate the temperature of the gas in Celsius if the pressure is changed to 2×10 to the power 4
Amahle Reply
How is energy being used in bonding?
Raymond Reply
what is acceleration
Syamthanda Reply
a rate of change in velocity of an object whith respect to time
Khuthadzo
how can we find the moment of torque of a circular object
Kidist
Acceleration is a rate of change in velocity.
Justice
t =r×f
Khuthadzo
how to calculate tension by substitution
Precious Reply
hi
Shongi
hi
Leago
use fnet method. how many obects are being calculated ?
Khuthadzo
khuthadzo hii
Hulisani
how to calculate acceleration and tension force
Lungile Reply
you use Fnet equals ma , newtoms second law formula
Masego
please help me with vectors in two dimensions
Mulaudzi Reply
how to calculate normal force
Mulaudzi
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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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