Math 0308/math 0310 Factoring Polynomials Worksheet With Answer Key - Lone Star College Montgomery, 2011
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3MATH 0308 / MATH 0310
Factoring Polynomials
Factoring the GCF
The Greatest Common Factor (GCF) is the largest factor that divides into each term of a
polynomial.
2
Example:
3x
+ 6xy + 9x = 3x(x + 2y + 3)
GCF = 3x
2
2
Factoring by Patterns
Difference of Squares
x
y
(
x y x y
)(
)
2
2
(Special Products)
Sum of Squares
x
y = prime, cannot be factored
3
3
2
2
Difference of Cubes
x
y
(
x y x
)(
xy y
)
3
3
2
2
Sum of Cubes
x
y
(
x y x
)(
xy y
)
2
2
2
x
2
xy y
(
x y
)
Trinomial Squares
2
2
2
x
2
xy y
(
x y
)
2
2
Difference of Squares
x
y
(
x y x y
)(
)
2
2
Example:
4x
16
= 4(x
4)
GCF = 4
= 4(x 2)(x + 2)
3
3
2
2
Sum of Cubes
x
+ y
= (x + y)(x
xy + y
)
3
3
3
Example:
x
+ 27
= (x
+ 3
)
2
= (x + 3)(x
3x + 9)
3
– y
3
= (x – y)(x
2
2
Difference of Cubes
x
+ xy + y
)
3
– 8
3
– 2
3
Example:
x
= x
2
= (x-2)(x
+ 2x + 4)
2
2
2
2
2
2
Trinomial Squares
x
2
xy y
(
x y
)
or
x
2
xy y
(
x y
)
2
– 6x + 9
Example:
x
The first and third terms are positive
2
2
The first and third terms are perfect squares: x
and 3
Twice their product is the middle term: 2 (x 3) = 6x Disregard the sign
2
2
– 6x + 9 = (x – 3)
Therefore, x
Use the sign of the middle term
2
Example:
9x
+ 6x + 1
The first and third terms are positive
The first and third terms are perfect squares: (3x)2 and 12
Twice their product is the middle term: 2 (3x 1) = 6x
2
2
Therefore, 9x
+ 6x + 1 = (3x + 1)
Use the sign of the middle term
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