1. Factoring Trinomials

2. Warm Up Multiply: 1. (x + 3)(x – 7) 2. (x – 6)(x + 5)

3. Math 2 Today’s Question:
How do I factor trinomials with a leading coefficient of one?

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

5. Ex 1. Factor the Trinomial Always look for a GCF First!!
x2 + 4x + 3
( )( )
GCF??... NO! x + 3 x + 1
What multiplies to equal x2
What #s multiply to equal 3?
x • x
3 and 1
continued

6. 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
3x + x = 4x  x

7. Ex.2) Factor the Trinomial
GCF??... NO! 6 x2
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 
2, 3
1, 6
x, x x + 2 x + 3 2x 3x

8. Ex. 3) Factor the Trinomial
GCF??... NO!
x2 – 2x – 3
( )( ) -3 x2 x - 3 x + 1
-3, 1
-1, 3
x, x
-3x 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 

9. Practice Factor the following: 1. x2 + 9x + 8 2. x2 – 12x + 10

10. 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)

11. 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)

12. Practice!! 2(x + 2) (x + 6) 3x(x + 5) (x – 2) x(x + 7) (x – 2)
Factor each
Polynomial !!!
Don’t forget the GCF!
2(x + 2) (x + 6)
3x(x + 5) (x – 2)
x(x + 7) (x – 2)
3(x + 5) (x + 4)
4(x – 4) (x + 3)
2x(x - 6)(x + 4)

13. Class work-begin Factoring WS
Homework-Finish Factoring WS