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View Full DocumentMath 1300
Section 4.2
1
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 square trinomials.
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
)
)(
(
2
2
b
a
b
a
b
a
+

=

is how a difference of squares polynomial is
factored.
Example 1:
Factor
x
2
– 25.
Example 2:
Factor 9
x
2
– 49.
Example 3:
2
4
100
x

Note:
There is
no
sum of squares factorization; that is, we can’t factor
a
2
+
b
2
.
Difference of Cubes
To find the pattern for the difference of cubes, the polynomial to factor must be a binomial, the
first term must be a variable to the third power (a.k.a. cubed) and a constant term must be
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 Spring '08
 Staff
 Math, Factoring, Factoring Polynomials, Polynomials

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