Objective The student will be able to:

1
ObjectiveThe student will be able to
factor quadratic trinomials. Trial and Error
Method SOL A.2c
Designed by Skip Tyler, Varina High School
2
Factoring ChartThis chart will help you to
determine which method of factoring to
use.Type Number of Terms

• 1. GCF 2 or more
• 2. Diff. Of Squares 2
• 3. Trinomials 3

3
Review (y 2)(y 4) Multiply using FOIL
or using the Box Method.Box Method
y 4 y y2 4y 2 2y
8 Combine like terms.

• FOIL y2 4y 2y 8
• y2 6y 8

4
1) Factor. y2 6y 8Put the first and last
terms into the box as shown.

• What are the factors of y2?
• y and y

5
1) Factor. y2 6y 8Place the factors outside
the box as shown.

• What are the factors of 8?
• 1 and 8, -1 and -8
• 2 and 4, -2 and -4

6
1) Factor. y2 6y 8Which box has a sum of
6y?
1
2
y
y
2y
8y
4y
8
4

• The second box works. Write the numbers on the
  outside of box for your solution.

y
7
1) Factor. y2 6y 8

• (y 2)(y 4)
• Here are some hints to help you choose your
  factors.
• 1) When the last term is positive, the factors
  will have the same sign as the middle term.
• 2) When the last term is negative, the factors
  will have different signs.

8
2) Factor. x2 - 2x - 63Put the first and last
terms into the box as shown.

• What are the factors of x2?
• x and x

9
2) Factor. x2 - 2x - 63 Place the factors
outside the box as shown.

• What are the factors of - 63?
• Remember the signs will be different!

10
2) Factor. x2 - 2x - 63Use trial and error to
find the correct combination!
x
- 3
x2
x
-3x
- 63
21
21x

• Do any of these combinations work?
• The second one has the wrong sign!

11
2) Factor. x2 - 2x - 63Change the signs of the
factors!
7
7x
- 9
-9x

• Write your solution.
• (x 7)(x - 9)

12
3) Factor. 5x2 - 17x 14Put the first and last
terms into the box as shown.

• What are the factors of 5x2?
• 5x and x

13
3) Factor. 5x2 - 17x 14

• What are the factors of 14?
• Since the last term is positive, the signs of the
  factors are the same! Since the middle term is
  negative, the factors must be negative!

14
3) Factor. 5x2 - 17x 14 When the coefficient
is not 1, you must try both combinations!
5x
- 2
5x
- 7
5x2
x
- 2x
5x2
x
- 7x
14
- 7
-35x
14
- 2
-10x

• Do any of these combinations work?
• The second one! Write your answer.

15
3) Factor. 5x2 - 17x 14

• (5x - 7)(x - 2)
• It is not the easiest of things to do, but the
  more problems you do, the easier it gets! Trust
  me!
• 4) Factor 2x2 9x 10
• (x 2)(2x 5)

16
5) Factor. 6y2 - 13y - 5

• (2y - 5)(3y 1)
• 6) 12x2 11x - 5
• (4x 5)(3x - 1)
• 7) 5x - 6 x2
• x2 5x - 6
• (x - 1)(x 6)