Factoring Trinomials

Warm Up

• Multiply:

• 1. (x + 3)(x – 7)

• 2. (x – 6)(x + 5)

• 3. (x + 2)(x + 9)

• 4. (x – 4)(x – 6)

Math 2

• Today’s Question:• How do I factor trinomials with a leading

coefficient of one?

Let’s Multiply

(x+2)(x+1)= x2 + x + 2x + 2= x2 + 3x + 2What if we wanted to “undo” Multiplying?Look at the result that we got above:x2 + 3x + 2How can I write this as a product of binomials?( )( )x x+ +2 1

Ex 1. Factor the TrinomialAlways look for a GCF First!!

• x2 + 4x + 3

( )( )x+ 3 1+x

GCF??... NO!GCF??... NO!

What #s multiply to equal 3?

3 and 1

What multiplies to equal x2

x • x

continued

Ex.1) Continued

(x + 3)(x + 1)

How do I know this is right? Look at the product of the outer and inner terms.Do they add to give you the middle term?YES….so you factored it correctly!

3x + x = 4x

3x

x

Ex.2) Factor the Trinomial

x2 + 5x + 6( )( )

So, do we use 2 and 3 or 1 and 6?Well…which ones will add to give you 5?2 and 3!! Check!3x + 2x = 5x

6

2, 3

1, 6

x2

x, xx+ 2 3+x

2x

3x

GCF??... NO!GCF??... NO!

Ex. 3) Factor the Trinomial

x2 – 2x – 3

( )( ) -3 x2

-3, 1

-1, 3

x, xx- 3 1+x

So, do we use -3 and 1 or -1 and 3?Well…which ones will add to give you -2?-3 and 1!! Check!x + -3x = -2x

-3x

x

GCF??... NO!GCF??... NO!

Practice

Factor the following:

1. x2 + 9x + 8

2. x2 – 12x + 10

3. x2 – 2x – 3

4. x2 + 8x + 15

Factoring with GCF

• *****Always look for a GCF first*****• Ex. 4x2 – 12x – 16• What is the GCF?• 4(x2 – 3x – 4)• Can we factor x2 – 3x – 4 more?• Are there two numbers that multiply to equal -4

and add to be -3?• x2 – 3x – 4 factors to (x – 4)(x + 1)• Final answer: 4(x – 4)(x + 1)

Factoring with GCF

• Example 2: 6x2 + 30x + 36• GCF?• 6• 6(x2 + 5x + 6)• Can be x2 + 5x + 6 factored?

x2 + 5x + 6 can be factored to (x + 3)(x + 2)• Answer: 6(x + 3)(x + 2)

Practice!!Practice!!2

3 2

3 2

2

2

3 2

1. 2 16 24

2. 3 9 30

3. 5 14

4. 3 27 60

5. 4 4 48

6. 2 4 48

x x

x x x

x x x

x x

x x

x x x

Factor eachPolynomial !!!

1.1.2(x + 2) (x + 2(x + 2) (x + 6)6)

2.2.3x(x + 5) (x – 3x(x + 5) (x – 2)2)

3.3.x(x + 7) (x – 2)x(x + 7) (x – 2)4.4.3(x + 5) (x + 3(x + 5) (x +

4)4)5.5.4(x – 4) (x + 4(x – 4) (x +

3)3)6.6.2x(x - 6)(x + 2x(x - 6)(x +

4)4)

Don’t forget the GCF!

Class work-begin Factoring WS

Homework-Finish Factoring WS