ObjectiveThe student will be able to:

factor quadratic trinomials.

Trial and Error Method

SOL: A.2cDesigned by Skip Tyler, Varina High School

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

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

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

as shown.

What are the factors of y2?

y and y

y2

+ 8

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

y2

+ 8

y

y

What are the factors of + 8?

+1 and +8, -1 and -8

+2 and +4, -2 and -4

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

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

y2

+ 8

y

y

y2

+ 8

y

y+ 1 + 2

+ 8 + 4

+ y

+ 8y + 4y

+ 2y

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.

x2

- 63

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

as shown.

What are the factors of x2?

x and x

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

x2

- 63

x

x

What are the factors of - 63?

Remember the signs will be different!

2) Factor. x2 - 2x - 63Use trial and error to find the correct

combination!

Do any of these combinations work?

The second one has the wrong sign!

x2

- 63

x

x

+ 21

- 3

+21x

-3x x2

- 63

x

x - 7

+ 9

-7x

+9x

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

Write your solution.

(x + 7)(x - 9)

x2

- 63

x

x + 7

- 9

+7x

-9x

5x2

+ 14

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

as shown.

What are the factors of 5x2?

5x and x

3) Factor. 5x2 - 17x + 14

5x2

+ 14

x

5x

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!

3) Factor. 5x2 - 17x + 14 When the coefficient is not 1, you must try

both combinations!

Do any of these combinations work?

The second one! Write your answer.

5x2

+ 14

x

5x

- 7

- 2

- 2x

-35x

5x2

+ 14

x

5x

- 2

- 7

- 7x

-10x

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)

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)