Factoring Worksheet With Examples Page 10
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2
b. 18c d
+ 12 c
d + 9cd
2
18c d
= 2 · 3 · 3 · c · d · d
Factor each monomial.
2
12 c
d = 2 · 2 · 3 · c · c · d
Circle the common prime factors.
9cd = 3 · 3 · c · d
GCF: 3 · c · d or 3cd
2
2
18c d
+ 12 c
d + 9cd = 3cd(6d) + 3cd(4c) + 3cd(3)
Rewrite each term using the GCF.
= 3cd(6d + 4c + 3)
Distributive Property
2
2
1
1
A.
16a + 4b
B.
3 p
q - 9p q
+ 36pq
Using the Distributive Property to factor polynomials having four or more
terms is called factoring by grouping because pairs of terms are grouped
together and factored. The Distributive Property is then applied a second
time to factor a common binomial factor.
EXAMPLE
Use Grouping
Factor 4ab + 8b + 3a + 6.
Factoring by
Grouping
4ab + 8b + 3a + 6
Sometimes you can
= (4ab + 8b) + (3a + 6)
Group terms with common factors.
group terms in more
than one way when
=
4b(a +
2)
+
3(a +
2)
Factor the GCF from each grouping.
factoring a polynomial.
For example, the
=
(a +
2)(4b +
3)
Distributive Property
polynomial in Example
2 could have been
factored in the
Factor each polynomial.
following way.
2
2
- 15x - 8x + 20
2
rs + 5s - r - 5
A.
6 x
B.
4ab + 8b + 3a + 6
= (4ab + 3a) +
(8b + 6)
Recognizing binomials that are additive inverses is often helpful when
= a(4b + 3) +
factoring by grouping. For example, 7 - y and y - 7 are additive inverses.
2(4b + 3)
By rewriting 7 - y as -1(y - 7), factoring by grouping is possible in the
= (4b + 3)(a + 2)
following example.
Notice that this result
is the same as in
Example 2.
EXAMPLE
Use the Additive Inverse Property
Factor 35x - 5xy + 3y - 21.
35x - 5xy + 3y - 21 = (35x - 5xy) + (3y - 21)
Group terms with common factors.
= 5x(7 - y) + 3(y - 7)
Factor the GCF from each grouping.
= 5x(-1)(y - 7) + 3(y - 7)
7 - y = -1(y - 7)
=
-5x(y -
7)
+
3(y -
7)
5x(-1) = -5x
=
(y -
7)(-5x +
3)
Distributive Property
Factor each polynomial.
2
3
3
A.
c - 2cd + 8d - 4
B.
3p - 2 p
- 18p + 27
427
Extra Examples at
Lesson 8-2 Factoring Using the Distributive Property
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