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§ 6.3
Factoring Trinomials of
the Form
ax
2
+
bx
+
c
and
Perfect Square Trinomials
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View Full Document MartinGay,
Beginning Algebra, 5ed
2
Factoring Trinomials
Returning to the FOIL method,
F
O
I
L
(3
x
+ 2)(
x
+ 4) =
3
x
2
+
12
x
+
2
x
+
8
=
3
x
2
+
14
x
+
8
To factor
a
x
2
+
b
x
+
c
into (#
1
·
x
+ #
2
)(#
3
·
x
+ #
4
), note
that
a
is the product of the two first coefficients,
c
is
the product of the two last coefficients and
b
is the
sum of the products of the outside coefficients and
inside coefficients.
Note that
b
is the sum of 2 products, not just 2
numbers, as in the last section.
MartinGay,
Beginning Algebra, 5ed
3
Factor the polynomial 21
x
2
– 41
x
+ 10.
Possible factors of 21
x
2
are {
x
, 21
x
} or {3
x
, 7
x
}.
Since the middle term is negative, possible factors of
10 must both be negative: {1, 10} or {2, 5}.
We need to methodically try each pair of factors until
we find a combination that works, or exhaust all of our
possible pairs of factors.
Factoring Polynomials
Continued.
Example:
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View Full Document MartinGay,
Beginning Algebra, 5ed
4
We will be looking for a combination that gives the sum of
the products of the outside terms and the inside terms equal
to

41
x
.
Factors
of 21
x
2
Resulting
Binomials
Product of
Outside Terms
Product of
Inside Terms
Sum of
Products
Factors
of 10
{
x
, 21
x
}{1, 10}(
x
–
1
)(
21
x
–
10
)
–10
x

21
x
– 31
x
(
x
–
10
)(
21
x
–
1
)
–
x

210
x
– 211
x
{
x
, 21
x
} {2, 5}
(
x
–
2
)(
21
x
–
5
)
–5
x

42
x
– 47
x
(
x
–
5
)(
21
x
–
2
)
–2
x

105
x
– 107
x
Factoring Polynomials
Continued.
Example continued:
Beginning Algebra, 5ed
5
Factors
of 21
x
2
Resulting
Binomials
Product of
Outside Terms
Product of
Inside Terms
Sum of
Products
Factors
of 10
(
3
x
–
5
)(
7
x
–
2
)

6
x

35
x

41
x
{3
x
, 7
x
}{1, 10}(
3
x
–
1
)(
7
x
–
10
)

30
x

7
x

37
x
(
3
x
–
10
)(
7
x
–
1
)

3
x

70
x

73
x
{3
x
, 7
x
} {2, 5}
(
3
x
–
2
)(
7
x
–
5
)

15
x

14
x

29
x
Factoring Polynomials
Continued.
Example continued:
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This note was uploaded on 06/10/2009 for the course MAC 1103 taught by Professor Prescott during the Spring '09 term at PascoHernando Community College.
 Spring '09
 prescott
 Algebra, Factoring, Factoring Trinomials

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