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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 a proficiency exam for the chapter "Factoring Polynomials".

Proficiency exam

( [link] ) The product is 27 a 3 + 9 a 2 + 9 a and a factor is 3 a . Find the other factor.

9 a 2 + 3 a + 3

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( [link] ) The product is 15 x n 5 y 3 n 2 . Find the other factor.

5 x n y 2 n 3

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

( [link] ) 14 x 2 y 4 b 28 x 2 y 3 b - 42 x 2 y 2

14 x 2 y 2 ( y 2 b + 2 y b + 3 )

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( [link] ) ( y 2 ) a ( y 2 ) c

( a + c ) ( y + 2 )

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( [link] ) 6 x 2 y 2 z 5 x 2 y 3 12 x y z 10x y 2

x y ( x y 2 ) ( 6 z + 5 y )

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( [link] ) 4 a 2 16 c 2

4 ( a + 2 c ) ( a 2 c )

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( [link] ) m 4 n 4

( m 2 + n 2 ) ( m + n ) ( m n )

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( [link] ) b 2 + 8 b + 16

( b + 4 ) 2

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( [link] ) 9 y 2 30 y 25

( 3 y 5 ) 2

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( [link] ) x 2 5x 15

not factorable

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( [link] ) x 2 x 30

( x 6 ) ( x + 5 )

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( [link] ) 4 x 6 36 x 4 80 x 2

4 x 2 ( x 2 5 ) ( x + 2 ) ( x 2 )

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( [link] ) 9 x 2 + 25 x 6

( 9 x 2 ) ( x + 3 )

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Questions & Answers

calculate molarity of NaOH solution when 25.0ml of NaOH titrated with 27.2ml of 0.2m H2SO4
Gasin Reply
what's Thermochemistry
rhoda Reply
the study of the heat energy which is associated with chemical reactions
Kaddija
How was CH4 and o2 was able to produce (Co2)and (H2o
Edafe Reply
explain please
Victory
First twenty elements with their valences
Martine Reply
what is chemistry
asue Reply
what is atom
asue
what is the best way to define periodic table for jamb
Damilola Reply
what is the change of matter from one state to another
Elijah Reply
what is isolation of organic compounds
IKyernum Reply
what is atomic radius
ThankGod Reply
Read Chapter 6, section 5
Dr
Read Chapter 6, section 5
Kareem
Atomic radius is the radius of the atom and is also called the orbital radius
Kareem
atomic radius is the distance between the nucleus of an atom and its valence shell
Amos
Read Chapter 6, section 5
paulino
Bohr's model of the theory atom
Ayom Reply
is there a question?
Dr
when a gas is compressed why it becomes hot?
ATOMIC
It has no oxygen then
Goldyei
read the chapter on thermochemistry...the sections on "PV" work and the First Law of Thermodynamics should help..
Dr
Which element react with water
Mukthar Reply
Mgo
Ibeh
an increase in the pressure of a gas results in the decrease of its
Valentina Reply
definition of the periodic table
Cosmos Reply
What is the lkenes
Da Reply
what were atoms composed of?
Moses 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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