1.
5x
2
+ 9x + 4
2.
6x
2
+ 7x
–
3
3.
4x
2
–
16xy + 7y
2
18

5.3.3: Factoring Trinomials with a Common Factor
The
first step
in any factoring process is to remove any
existing common factors.
It may be necessary to combine common-term factoring
with other methods (such as factoring a trinomial into a
product of binomials) to completely factor a polynomial.
Examples:
Factor the following trinomials.
1.
2x
2
–
16x + 30
2.
6x
3
+ 15x
2
y
–
9xy
2
19

5.3.3: Completely Factor a Trinomial
One final note:
When factoring, we require that all
coefficients be integers. Given this restriction,
not
all
polynomials are
factorable
over the integers.
Examples:
Factor the following trinomials.
1.
x
2
–
9x + 12
20

5.4: Factoring Trinomials: The
ac
Method
Objectives:
5.4.1: Use the
ac
test to determine factorability.
5.4.2: Factor a trinomial using the
ac
method.
5.4.3: Completely factor a trinomial
21

5.4.1: Use the
ac
Test to Determine Factorability.
Some students prefer the method of this section (called the
ac
method
)
because it yields the answer in a systematic way
.
Not all trinomials can be factored. To discover whether a
trinomial is factorable, we try the
ac test.
22

5.4.1: Use the
ac
Test to Determine Factorability.
Examples:
Use the
ac
test to determine which of the following
trinomials can be factored
.
Find
the
values of
m and n
for
each trinomial that can be factored.
1.
x
2
–
3x
–
18
2.
x
2
–
24x + 23
3.
x
2
–
11x + 8
4.
2x
2
+ 7x
–
15
23

5.4.2: Factor a Trinomial Using the
ac
Method.
Examples:
Factor using the ac method
1.
2x
2
–
13x
–
7
2.
6x
2
–
5x
–
6
24

5.4.3: Completely Factor a Trinomial
The
first step
in any factoring process is to remove any
existing common factors.
Examples:
Factor the following trinomials.
1.
3x
2
–
12x
–
15
25

5.5: Strategies in Factoring
Objectives:
5.5.1: Recognize factoring patterns.
5.5.2: Apply appropriate factoring strategies.
26

5.5.1: Recognize factoring patterns.
1.
Always look for a greatest common factor. If you find a GCF (other
than 1), factor out the GCF as your first step.
2.
Now look at the number of terms in the polynomial you are trying
to factor.
A.
If the polynomial is a
binomial, consider the special binomial
formulas.

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- Fall '18
- jane
- Accounting, Quadratic equation, Elementary algebra