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. Grouping 4

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

Algebraic Method

Remember: (y + 2)(y + 4)

= y2 + (2+4)x + (2*4)

= y2 + 6x + 8

You multiply to get the constant term and add to get the linear term.

2) Try one x2 + 15x + 36

What do I multiply to get 36?

1 x 36 2 x 18 3 x 12 4 x 9 6 x 6

-1 x -36 -2 x -18 -3 x -12 -4 x -9 -6 x -6

Which set of numbers adds to give me 15?

Answer: (x + 3)(x + 12)

Example: Factor

Find 2 numbers a and b that multiply together to get 15 and

add up 8. The numbers are:

Now factor using the signs of the 2 numbers before them.

1582 xx

)5)(3( xx

Factor

Find 2 numbers a and b that multiply together to get +8 and

add up -6. The numbers are:

Now factor using the signs of the 2 numbers before them.

862 xx

)4)(2( xx

Factor

Find 2 numbers a and b that multiply together to get -24 and add up 2. The

numbers are:

Now factor using the signs of the 2 numbers before them.

2422 xx

)4)(6( xx

Factor

Find 2 numbers a and b that multiply together to get -14 and add up -5. The

numbers are:

Now factor using the signs of the 2 numbers before them.

1452 xx

)7)(2( xx

Summary for the signs for factoring a trinomial:

If the sign of last is + then the 2 numbers have the same sign, which is the same as the

middle sign.

If the sign of last is - then the 2 numbers have opposite signs with the sign of middle going

with the larger (greatest absolute value)

lastxmiddlex )(2

Examples:

__)__)((20122 xxxx

__)__)((20122 xxxx

__)__)((2422 xxxx

__)__)((2422 xxxx