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Factoring Trinomials
Diamond Box Method
Factoring
5/17/2012
Medina
1
Solving Quadratic Equations by
factoring
Step 1: Write equation in
Example:
Standard Form
x² + 4x + 3 = 0
ax² + bx + c = 0
Step 2: Using factoring rules to
factor GCMF
★NOTE: If the equation is
Diamond
Box
not factorable you must
solve using the quadratic
formula, it does not mean
no solution.
Step 3: Using the zero product
property to solve for x
Diamond-Box Method
• https://www.youtube.com/watch?v=E8-hBg7LvRs
4/13/2010
Medina
3
Trinomials
Step 1: Standard Form
2
Step 2:
x  7x  12
12
 1 x  7x 12
12
x  3 
x
 4
3
2
1.
2.
3.
 x  3 x  4 
5/17/2012
Medina
4.
4
7
Factor out the GCF
Set up Diamond Problem
Set up Box to find common
factors
Bring down GCF & Factors
4
Solving Quadratic Equations by
factoring
Step 3: Solve for x using the zero
product property
( x  3)( x  4)  0
x3 0
3 3
x  3
x40
4 4
x  4
Trinomials
Step 1: Standard Form
x 2  12x  35
1x
Step 2:
x
2

7
12x 35
x
 7
5
12
* Note : When the first number is a negative, factor out the (- ) sign
 5
1.
 x  7  x  5 
5/17/2012
35
2.
3.
4.
Medina
Factor out the GCF other
than 1
Set up Diamond Problem
Set up Box to find common
factors
Bring down GCF & Factors
6
Solving Quadratic Equations by
factoring
Step 3: Solve for x using the zero
product property
( x  7)( x  5)  0
x7  0
7  7
x7
x 5  0
5  5
x5
Diamond-Box Method
• https://www.youtube.com/watch?v=cvaW5p0vSzw
4/13/2010
Medina
8
Trinomials
Step 1: Standard Form
4x 2  32x  28
Step 2:
4  1 x  8x
x
x
 1
22

7
7
7
 7
1
8
1.
2.
3.
x  7  x  1
5/17/2012
7
Medina
4.
Factor out the GCF other
than 1
Set up Diamond Problem
Set up Box to find common
factors
Bring down GCF & Factors
9
Solving Quadratic Equations by
factoring
Step 3: Solve for x using the zero
product property
★ The GCF
4( x  7)( x  1)  0
does not have a
variable to
x7 0
x 1  0
solve for
7 7
1  1
therefore we do
x

1
x


7
not set it equal
to 0.
Trinomials
Step 1: Standard Form
2
2x  26x  72
Step 2:


9
22
x
2 1  13x 36
x
4
x
 9
4
13

1.
x  9 x  4 
5/17/2012
36
Medina
2.
3.
4.
Factor out the GCF other
than 1
Set up Diamond Problem
Set up Box to find common
factors
Bring down GCF & Factors
11
Solving Quadratic Equations by
factoring
Step 3: Solve for x using the zero
product property
★ The GCF
2( x  9)( x  4)  0
does not have a
variable to
x9  0
x40
solve for
9 9
4 4
therefore we do
x

4
x


9
not set it equal
to 0.
Trinomials
22
3xx  10x 8
3
8
3x
 2
x
4

x
* Note : When the first number is a negative, factor out the (- ) sign
x
1.
 x  4 3x  2
5/17/2012
24
12
2
10
2.
3.
4.
Medina
Factor out the GCF other
than 1
Set up Diamond Problem
Set up Box to find common
factors
Bring down GCF & Factors
13
Solving Quadratic Equations by
factoring
Step 3: Solve for x using the zero
product property
( x  4)(3 x  2)  0
x40
4 4
x  4
3x  2  0
2  2
3x  2
3 3
2
x
3
Solving Quadratic Equations by
factoring
Step 1: Write equation in Standard Form
ax² + bx + c = 0
x  5 x  6
Step 2: Using factoring rules to factor
6 6
2
x  5x  6  0
Step 3: Using the zero product
property to solve for x
( x  2)( x  3)  0
2
x20
2  2
x  2
x3  0
3  3
x  3
Solving Quadratic Equations by
factoring
Step 1: Write equation in Standard Form
ax² + bx + c = 0
x  6 x  27
27  27
2
x  6 x  27  0
( x  9)( x  3)  0
Step 2: Using factoring rules to factor
Step 3: Using the zero product
property to solve for x
x( x  6)  27
x 9  0
9  9
x9
2
x3  0
3  3
x  3
Solving Quadratic Equations by
factoring
Real World Problem
Area = l w
Area = 21in²
Area = x(x+4)
21 = x(x+4)
But distance can
only be positive,
therefore x =3
21  x  4 x
21
 21
2
0  x  4 x  21
( x  3)( x  7)  0
2
x 3  0 x  7  0
 3  3 7  7
x3
x  7