This document provides examples and steps for factoring trinomials using the "slide and divide" method. It demonstrates factoring trinomials of the form ax^2 + bx + c through 4 examples, showing the steps of finding the greatest common factor, "sliding" terms to group like terms, factoring, dividing and simplifying, and "pushing back" the factors. Exercises are assigned from the green algebra book problems 25-39 odds on page 328.

1. 1. Check your grade
2. Be ready to take
notes when the bell
rings.
Objective: SWBAT factor
trinomials of the form
using the “slide and divide”
method
2
ax bx c+ +

2. Example #1 Factor 2
2 11 15x x+ +
1. GCFs? 2. “Slide” 3. Factor
4.Divide & simplify 5. “Push back” 6. Check
2
2 11 15x x+ +
1 1 1
No!
2
2 11 15x x+ +
2
11 30x x+ +
2
11 30x x+ +
( )( )x x
( 6)( 5)x x+ +
6+5=11 6*5=30
( 6)( 5)x x+ +
2 2
5
( 3)( )
2
x x+ +
5
( 3)( )
2
x x+ +
( 3)(2 5)x x+ +
( 3)(2 5)x x+ +
2
2 5 6 15x x x+ + +
2
2 11 15x x+ +
Correct

3. Example #2 Factor 2
3 4x x− −
2
3 4x x− −
No GCF
“Slide”
2
12x x− −
( )( )x x
Factor
( 3)( 4)x x+ −
Divide & simplify
( 3)( 4)x x+ −
3 3
4
( 1)( )
3
x x+ −
“Push back”
4
( 1)( )
3
x x+ −
( 1)(3 4)x x+ −
Check:
( 1)(3 4)x x+ −
2
3 4 3 4x x x− + −
2
3 4x x− −

4. Example #3 Factor
1. GCFs? 2. “Slide” 3. Factor
4.Divide & simplify 5. “Push back” 6. Check
4 3 2
12 42 18x x x+ +
4 3 2
12 42 18x x x+ +
Yes!
2
6x 2
6x 2
6x
6+1=7 6*1 = 6
2 2
6 (2 7 3)x x x+ +
2 2
6 (2 7 3)x x x+ +
( )2 2
6 7 6x x x+ +
( )2 2
6 7 6x x x+ +
2
6 (x x )( )x
2
6 ( 6)( 1)x x x+ +
2
6 ( 6)( 1)x x x+ +
2 2
2 1
6 ( 3)( )
2
x x x+ +
2 1
6 ( 3)( )
2
x x x+ +
2
6 ( 3)(2 1)x x x+ +
2
6 ( 3)(2 1)x x x+ +
2 2
6 (2 6 1 3)x x x x+ + +
2 2
6 (2 7 3)x x x+ +
4 3 2
12 42 18x x x+ +

5. Example #4 Factor 3 2
12 22 8x y x y xy− +
3 2
12 22 8x y x y xy− +
2xy 2xy 2xy GCF
2
2 (6 11 4)xy x x− +
“Slide”2
2 ( 11 24)xy x x− +
Factor2 ( 8)( 3)xy x x− −
6 6
2 ( 8)( 3)xy x x− −
Divide and simplify
4 1
2 ( )( )
3 2
xy x x− −
4 1
2 ( )( )
3 2
xy x x− −
Push back
2 (3 4)(2 1)xy x x− −
Check:
2 (3 4)(2 1)xy x x− −
2
2 (6 3 8 4)xy x x x− − +
2
2 (6 11 4)xy x x− +
3 2
12 22 8x y x y xy− +

6. Write a 2-3 sentence summary at
the bottom of your notes
Exercises
p. 328 #25-39 odds (GREEN ALGEBRA
BOOK)

7. Write a 2-3 sentence summary at
the bottom of your notes
Exercises
p. 328 #25-39 odds (GREEN ALGEBRA
BOOK)