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HIGH SCHOOL
MATH
FACTORING
Ask Yourself the following
questions…
1
Is there a common factor?
Example:
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6x2 + 8x
= 2x (
)
N
G
= 2x ( 3x + 4 )
1. What is the common factor?
2. Remove the common factor.
3. Divide each elements of the
expression by the common
factor.
Ask Yourself the following
questions…
2
Is there the difference between
two squares?
Example:
F
4x2 – 81
=if something
(
)(
How to determine
is a “Difference
of)Two
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Squares”
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1.
Is the first term=
a perfect(2x
square?9 ) (
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2. Is the second term a perfect square?
3. Is there a negative sign in the middle?
I
=
2x
9)
(2x + 9 ) ( 2x - 9 )
1. Use
the Two
Factor Method
Then
the expression
is a Difference of Two Squares”
2. Take the square root of the 1st and the square root of the 2nd
3. Use opposite signs in the middle
Ask Yourself the following
questions…
3
Is there a perfect square?
Example:
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x2 + 8x + 16
( is a “Perfect
)2 Square”
How to determine if =
something
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G
2.
3.
4.
= square?
(x
Is the first term a perfect
Is the last term a perfect square?
(x+
Recall: ax2 + bx + c=
=0
Does
½ bup
)2 the
= c factor
?
1. (Set
4 )2
4 )2
2. Take the square root of the 1st term and the
Then
the root
expression
is aterm
Perfect Square”
square
of the last
3. Use the sing of the middle term and place it
between the square roots
To determine the Signs of the
To determine the Values of the
Factors
Second Term
Recall: ax2 + bx + c = 0
Recall: ax2 + bx + c = 0
1. Consider the sign of the “c” term
1. What two numbers multiplied
2. If the sign is + then both signs will
together will give the “c” term
be the SAME and the factors will
*
=c
both have the sign of the “b” term
2. What same two numbers will give
4 will
Is the coefficient
of the x2’d term = 1?
3. If the sign is – then both signs
the “b” term
be DIFFERENT and the higher
+
=b
number will take the sign of the “b”
Example:
term
F
Ask Yourself the following
questions…
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1. Use the two factor method
x2 – 7x + 10
=(
)(
)
=(x
)(x
)
=(x- )(x- )
=(x-5)(x-2)
2. Factor the 1st term of the expression
3. Determine the signs of the factors
4. Determine the values of the2nd term
Recall !
6x2 + 5x – 4
Recall !
Ask Yourself the following
6x + 5x – 4
questions…
2
1. The signs will be different
2. The larger number will be
+
5
1. What 2 # ’ s multiplied together
will give (6 * -4), -24 ?
2. What same 2 # ’ s added
together will give 52?
Is the coefficient of the x ‘ d term ≠ 1
Example:
6x2 + 5x - 4
= 6x2 +5x
-4
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= 6x2 + 8x – 3x - 4
= 2x (3x + 4 ) – 1 (3x + 4)
= (3x + 4 ) (2x - 1)
1. Factor by “Grouping”
2. Determine the factors of the middle term
3. Remove the common factor from the 2 groups
4. Remove the binomial Common Factor
F
A
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1
Is there a common factor?
2
Is there the difference of two squares?
3
Is there a perfect square?
4
Is the coefficient of the x2’d term = 1?
5
Is the coefficient of the x2’d term ≠ 1?