Download factoring packet

November 11th
Factoring
Trinomials with a Leading
Coefficient of NOT 1
Swing and Divide
Happy Birthday to:
Cubby Wendt
&
Brianna Fabby
9.6 Factoring with
Swing and Divide
Factor trinomials with a
leading coefficient NOT
equal to 1.
EX 1:
2x2 – 11x + 5
How: Swing and Divide
Solution:
2x2 – 11x + 5
Step 1: Swing the
leading coefficient to
the back and multiply
x2 – 11x + 10
9.6 Factoring with
Swing and Divide
Factor trinomials with a
leading coefficient NOT
equal to 1.
How: Swing and Divide
EX 1:
2x2 – 11x + 5
Solution:
x2 – 11x + 10
Step 2: Factor the
10
trinomial using a T-chart
-1 -10
like last class.
-2 -5
(x – 1)(x – 10)
9.6 Factoring with
Swing and Divide
Factor trinomials with a
leading coefficient NOT
equal to 1.
EX 1:
2x2 – 11x + 5
How: Swing and Divide
Solution:
x2 – 11x + 10 =
(x – 1)(x – 10)
2
2
(x – 1)(x – 5)
2
Step 3: Divide the
numbers by what you
“swung”. Reduce what
you can.
9.6 Factoring with
Swing and Divide
Factor trinomials with a
leading coefficient NOT
equal to 1.
EX 1:
2x2 – 11x + 5
How: Swing and Divide
Solution:
x2 – 11x + 10 =
Step 4: Swing the
(x – 1)(x – 5)
denominator to the front
2
of that binomial.
(2x – 1)(x – 5)
9.6 Factoring with
Swing and Divide
Factor trinomials with a
leading coefficient NOT
equal to 1.
EX 2:
5n2 + 2n – 3
How: Swing and Divide
Solution:
5n2 + 2n – 3
Step 1: Swing the
leading coefficient to
the back and multiply
n2 + 2n – 15
9.6 Factoring with
Swing and Divide
Factor trinomials with a
leading coefficient NOT
equal to 1.
How: Swing and Divide
EX 2:
5n2 + 2n – 3
Solution:
n2 + 2n – 15
-15
Step 2: Factor the
1 -15
trinomial using a T-chart
-1 15
like last class.
3
-5
-3 5
(n + 5)(n – 3)
9.6 Factoring with
Swing and Divide
Factor trinomials with a
leading coefficient NOT
equal to 1.
EX 2:
5n2 + 2n – 3
How: Swing and Divide
Solution:
n2 + 2n – 15 =
(n + 5)(n – 3)
5
5
(n + 1)(n – 3)
5
Step 3: Divide the
numbers by what you
“swung”. Reduce what
you can.
9.6 Factoring with
Swing and Divide
Factor trinomials with a
leading coefficient NOT
equal to 1.
How: Swing and Divide
EX 2:
5n2 + 2n – 3
Solution:
n2 + 2n – 15 =
Step 4: Swing the
(n + 1)(n – 3)
denominator to the front
5
of that binomial.
(n + 1)(5n – 3)
Your turn!
EX 3: f(x) = 3x2 – 5x + 2
f(x) = (3x – 2)(x – 1)
Your turn!
EX 4:
y = 2m2 + m – 21
y = (2m + 7)(m – 3)
Types of Factoring So Far….
• Take out a GCF
10x2 – 12x
=
2x(5x – 6)
• Trinomials with leading coefficient = 1
x2 – 5x + 4
=
(x – 4)(x – 1)
• Trinomials with leading coefficient = 1
2x2 – 5x – 3 =
(2x + 1)(x – 3)
For some problems more than one type
of factoring must be used.
Example:
2x2 + 20x + 32
This is a trinomial with a leading
coefficient of 2, so maybe we should
use swing and divide -- but there is
also a GCF of 2. Which should we do
first?
Always do GCF first
EX 5:
2x2 + 20x + 32
= 2(x2 + 10x + 16)
= 2(x + 8)(x + 2)
Homework
WS
Homework
pg 596 9-12, 15-19, 22,