Lesson 6-5
Factoring ax2 + bx + c
Standard 11.0
Apply basic factoring techniques to second degree
polynomials
Taken from:
Rebecca Renken, Mathematics Department, Francis Howell High School
Example 1
• Factor 17x + 10 + 3x2
• Before factoring a trinomial it must be written in
descending order
• You must always look for the greatest common
factor first…it may be a negative.
• The coefficient of the squared term must be
positive.
• If the coefficient of the squared term is greater
than one that is what tells you to use the box and
diamond method
Example 1 Solution
Box and Diamond Method
•Factor 17x + 10 + 3x2  3x2 + 17x + 10, no
greatest common factor
•Draw a box put the first and last term diagonal
from each other
•Then multiply the coefficients together and this
will give you the number for the north
3x2
10
Example 1 Solution
Box and Diamond Method
3x2 + 17x + 10
3x2∙10 = 30x2
What can you multiply to get 30 that adds up to 17?
30
3x2
10
17
The
coefficient
of the
middle term
is in the
south
Example 1 Solution
Box and Diamond Method
3x2 + 17x + 10
3x2∙10 = 30x2
What can you multiply to get 30 that adds up to 17?
Put those same two terms in your box multiplied by the
variable
30
3x2
2
15
10
17
Example 1 Solution
Box and Diamond Method
3x2 + 17x + 10
Now factor out the greatest common factor from each row and
column
The signs from your diamond apply to the box
3x2
30
15x
2
15
2x
10
17
Example 1 Solution
Box and Diamond Method
3x2 + 17x + 10
Now factor out the greatest common factor from each row and
column
The signs from your diamond apply to the box
3x
x
+5
3x2
15x
30
2
15
+2
2x
10
The answer is (3x + 2)(x + 5)
17
Example 2
•Factor 12x2 + x - 6
Example 2
•Factor 12x2 + x – 6
3x
4x
+3
12x2
9x
-2
-72
-8x
-8
-6
•The answer is (4x + 3)(3x – 2)
9
1
Example 3
•Factor 30x2 -23x +3
•The answer is
Example 3
•Factor 30x2 -23x +3
5x
6x
-1
30x2
-5x
-3
90
-18x
-5
3
•The answer is (6x - 1)(5x – 3)
-18
-23
Things to Remember
• Always check for the GCF…it might be negative.
• The signs of the numbers in the “west” and “east”
indicate the signs that must be in your
parentheses.
• Check your work by using the FOIL method.
Burning Questions??