4
@12 Factoring out the GCF
%3
^1
To factor a polynomial, find its 
Greatest Common Factor (GCF).  
The GCF is the lowest term that is a 
factor of all numbers and variables in 
a problem.  
You must look at both the coefficients 
and the variables.  
^2
First, factor out the largest common 
factor of the coefficients.
^3
Then factor out the lowest power of the 
common variables.  
Write the common factors of the 
coefficients and variables as a product 
outside the parentheses.
~
%3
^1
To factor a polynomial, find its 
Greatest Common Factor (GCF).  
The GCF is the lowest term that is a 
factor of all numbers and variables in 
a problem.  
You must look at both the coefficients 
and the variables.  
^2
First, factor out the largest common 
factor of the coefficients.
^3
Then factor out the lowest power of the 
common variables. 
Write the common factors of the 
coefficients and variables as a product 
outside the parentheses.
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@22 Special Factorizations
%4
^1 
If a polynomial represents the 
difference of two squares both terms 
will be perfect squares.
^2
First, find the square root of the 
first term.
^3
Find the square root of the second term 
(disregarding the negative sign).
^4
The first factor is the sum of the two 
roots.  
The second factor is the difference of 
the two roots.
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%5
^1
Learn to recognize a trinomial square.  
The first and third terms will be 
perfect squares.  
The middle term will be twice the 
product of the two square roots.  
^2
First, find the square root of the 
first term.
^3
Find the square root of the third term.  
^4
Check to see if the middle term 
(disregarding its sign) is twice the 
product of the two square roots.
^5
The sign of each term has the same sign 
as the middle term of the perfect 
square trinomial.  
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@32 Factoring Trinomials
%4
^1
If the term in which the variable is 
squared (the quadratic term) has a 
coefficient of 1, use the following 
method.
^2
First factor the quadratic term.
^3
Find two numbers whose product is the 
last term (the constant) and whose sum 
is the coefficient of the middle term 
(the linear term).
^4
Form two binomial factors, each 
containing a variable factor and a 
number factor.
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%6
^1
If the coefficient of the quadratic 
term is not 1, use the following 
method.
^2
Multiply the constant (the last term) 
by the coefficient of the quadratic 
term (the first term).
^3
Find the two factors of this product 
whose sum is the coefficient of the 
linear term (the middle term).
^4
Using these two numbers as 
coefficients, rewrite the single linear 
term as two terms.
^5
Factor out the GCF of the first two 
terms; then factor out the GCF of the 
second two terms.
^6
Use the common binomial in parentheses 
as the first binomial factor in the 
answer.  
Use the two terms outside the 
parentheses as the second binomial 
factor in the answer.
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@42 Factoring Completely
%3
^1
Factor each polynomial completely, 
using one or more of the factoring 
methods you have learned.
^2
Always begin by factoring out any GCF 
(other than 1).  
^3
If possible, factor the remaining 
polynomial as either the difference of 
two squares or a trinomial square.
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%7
^1
Factor each polynomial completely, 
using one or more of the factoring 
methods you have learned.
^2
Always begin by factoring out any GCF 
(other than 1).
^3
Factor the remaining trinomial.
Multiply the constant (the last term) 
by the coefficient of the quadratic 
term (the first term).
^4
Find the two factors of this product 
whose sum is the coefficient of the 
linear term (the middle term).
^5
Using these two numbers as 
coefficients, rewrite the single linear 
term as two terms.
^6
Factor out the GCF of the first two 
terms; then factor out the GCF of the 
second two terms.
^7
The first factor in the final answer is 
the GCF of the original expression.  
Use the common binomial in parentheses 
as the second factor. 
Use the two terms outside the 
parentheses as the second binomial 
factor in the answer. 
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