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Section 4.2  Special Polynomials
Patterns
Certain polynomials can be factored by finding a pattern.
This section deals with four special
patterns for factoring polynomials:
difference of squares, difference of cubes, sum of cubes, and
perfect squares
Difference of Squares
The
difference of squares
pattern can be identified by looking at the polynomial.
It must be a
binomial, the first term must be a variable to the second power (a.k.a. squared) and a constant
term must be subtracted from it.
There is no firstorder variable term in a differenceofsquares
polynomial.
The formula is:
)
)(
(
2
2
b
a
b
a
b
a
+

=

Example:
Factor
x
2
– 25.
This binomial has its first term is
x
2
, a secondorder monomial.
The only other term is 25,
just a constant.
This means
x
2
– 25 can be factored using the difference of squares pattern, so
x
2
– 25 = (
x
)
2
– (5)
2
= (
x
– 5)(
x
+ 5).
To check, we can multiply the factored form back together using the FOIL method:
(
x
– 5)(
x
+ 5) =
x
2
+ 5
x
– 5
x
– 25 =
x
2
– 25.
Example:
Factor 9
x
2
– 25.
This binomial’s highest order monomial is
9x
2
; the other monomial is the constant 25, so we
can factor 9
x
2
– 25 using the difference of squares method:
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 Spring '08
 Staff
 Factoring, Factoring Polynomials, Polynomials

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