Factoring Using the Distributive Property

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Factoring Using the Distributive Property
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Factoring a Polynomial Using The Distributive
Property
Factoring a polynomial expression involves
re-writing the expression as a product of two or
more factors.
Sometimes expressions can be factored using the
Distributive Property. In essence, you are
reversing the steps taken when multiplying
factors using the Distributive Property.
For example, the polynomial 6a 6b can be
re-written as the product of the factors 6 and (a
- b).
To factor using the Distributive Property, you
should factor out the Greatest Common Factor
(GCF).
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Example 1
Factor the following polynomial
8x 12y
8x

12y
2 2 2 x
2 2 3 y
GCF is 2 2 4
Factored Form 4(2x 3y)
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Example 2
Factor the following polynomial
24x 48y
24x

48y
2 2 2 3 x
2 2 2 2 3 y
GCF is 2 2 2 3 24
Factored Form 24(x 2y)
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Example 3
Factor the following polynomial
4xy3 16x2y2
4xy3

16x2y2
2 2 x y y y
2 2 2 2 x x y y
GCF is 2 2 x y y 4xy2
Factored Form 4xy2 (y 4x)
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Example 4
Factor the polynomial
12p3q2 - 18p2q2 30pq
12p3q2
-
18p2q2

30pq
2 2 3 p p p q q
2 3 5 p q
2 3 3 p p q q
GCF is 2 3 p q 6pq
Factored Form 6pq (2p2q - 3pq 5)
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Example 5
Factor the following polynomial
9a 18b
9a

18b
3 3 a
2 3 3 b
GCF is 3 3 9
Factored Form 9 (a 2b)
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Factoring a Polynomial Using The Distributive
Property
Note When a variable is contained in each term
of a polynomial, you can factor it out using the
lowest exponent contained in any term for that
variable.
For example, in factoring the following
polynomial, the variable c is contained in each
term. The lowest exponent for the variable c
in any term is 3. The factored form should
therefore include c3
14c3 42c5 49c4
Factored Form 7c3 (2 6c2 7c)
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Examples
Factor the following polynomials
7c3 7c4
7c3 (1 c)
c3 c4
c3 (1 c)
12xy 6y
6y (2x 1)
30mn2 m2n 6n
n (30mn m2 6)
9x2 3x
3x (3x 1)
45x3 15x2
15x2 (3x - 1)
12mn 80m2
4m (3n 20m)