Math 10-C George McDougall High School NOTE: Props to Ms. Somerville for allowing me to adapt your notes!

 Step 1: Multiply the

F

IRST terms in the brackets.

(

x

 2 )(

x

 4 ) 

x

2

 Step 2: Multiply the

O

UTSIDE terms.

(

x

 2 )(

x

 4 ) 

x

2  4

x

 Step 3: Multiply the

I

NSIDE terms.

(

x

 2 )(

x

 4 ) 

x

2  4

x

 2

x

 Step 4: Multiply the

L

AST terms.

(

x

 2 )(

x

 4 ) 

x

2  4

x

 2

x

 8

 Step 5: Collect like terms.



x

2  4

x

 2

x

 8 

x

2  6

x

 8

( 3

x

 2 )(

x

 4 ) ( 3

x

 2 )(

x

 4 )  3

x

2  12

x

 2

x

 8  3

x

2  14

x

 8

( 3)(

x

 6) (6

x

 7)(2

x

 2)

Math 10-C George McDougall High School

Factoring Simple Trinomials

x

2 + 10 x + 16 = (x + 2)(x + 8)

Check by FOILing

= x 2 + 8x + 2x + 16 = x 2 + 10x + 16

x

2 + 9x + 20 = (x + 5)(x + 4)

x

2 + 5x + 4 = (x + 4)(x + 1)

x

2 + 11x + 24 = (x + 8)(x + 3) What relationship is there between product form and factored form?

Factoring Simple Trinomials Many trinomials can be written as the product of 2 binomials.

Recall: (x + 4)(x + 3) = x 2 + 3x + 4x + 12 = x 2 + 7x + 12

The

middle term

of a simple trinomial is the

SUM

last two terms of the binomials.

of the The

last term

of a simple trinomial is the

PRODUCT

the last two terms of the binomials.

of Therefore this type of factoring is referred to as

SUM-PRODUCT

!

To factor trinomials, you ask yourself…

x12 +7

1,12 13 2,6 8 3,4 7

x

2

+ 7x + 12

(x + 3)(x + 4)

Factor:

x

2

– 8x +12

( x – 2)( x – 6)

x 12

1, 12 -1, -12 2, 6 -2, -6

– 8

13 -13 8 -8

Factor:

m

2

– 5m -14

(m + 2) (m – 7)

x (-14)

-1, 14 1, -14 -2, 7 2, -7

-5

13 -13 5 -5

Factor:

x

2

- 11x + 24 x

2

+ 13x + 36 x

2

- 14x + 33

Factor: x 2 + 12x + 32 x 2 - 20x + 75 x 2 + 4x – 45 x 2 + 17x + 72 x 2 - 7x – 8

Factor:

- 5t – 3t

2

+ 15 + 4t

2

– 3 - 3t

STEP 1: Combine Like terms t 2 – 8t +12 ( x – 2 )( x – 6) x 12 1, 12 -1, -12 2, 6 -2, -6 - 8 13 -13 8 -8

Factor:

7q

2

– 14q - 21

7 ( q 2 –2q –3) 7 ( q – 3)( q + 1) STEP 1: Pull out the GCF -3 -1, 3 -3, 1 -2 2 -2

To Summarize: 1. Always check to see if you can simplify first!

2. Then check to see if you can pull out a common factor.

3. Write 2 sets of brackets with x in the first position.

4. Find 2 numbers whose sum is the middle coefficient, and whose product is the last term.

5. Check by foiling the factors.

ex. 2

x

2  14

x

 20  2(

x

2  7

x

 10)

common factor?

 2(

x

 5)(

x

 2) + = 7 x = 10 5, 2 ex.

3

x

2  3

x

 60  3(

x

2 20)

common factor?

 3(

x

 4)(

x

 5) + = 1 x = -20 -4, 5

How could we factor this using algebra tiles? 1.

2.

Create a rectangle using the exact number of tiles in the given expression.

Remember that a trinomial represents area – two binomials multiplied together.

3.

4.

What is the width and length of the rectangle?

These are the FACTORS of the original rectangle.

x + 3 Does that make sense?

x + 2 (x+3)(x+2)

1. Create a rectangle using the exact number of tiles in the given expression.

2. Remember that a trinomial represents area – two binomials multiplied together.

3. What is the width and length of the rectangle?

x

4. These are the FACTORS of the original rectangle.

2  3

x

 2

x

2  4

x

 4