1. Factoring ax2 + bx + c Objective:
Students will use factor trinomials of the
form ax2 + bx + c.

2. Algebra Standards:
11.0 Students apply basic factoring techniques to second
and simple third degree polynomials. These techniques
include finding a common factor to all of the terms in a
polynomial and recognizing the difference of two squares,
and recognizing perfect squares of binomials.
14.0 Students solve a quadratic equation by factoring or
completing the square.

3. a) 2x + 12 e) -6x2 – 14x 2 ( ) x + 6 -2x ( ) 3x + 7 b) 8x – 12 f) 4x2
#1 Factor a) 2x
+ 12 e)
-6x2
– 14x 2
( ) x
+ 6
-2x
( ) 3x
+ 7 b) 8x
– 12 f)
4x2
– 4x 4
( ) 2x
– 3 4x
( ) x
– 1 c)
4x2
+ 12x g)
-x2
– 20x 4x
( ) x
+ 3 -x
( ) x
+ 20 d)
-3x
+ 21 -3
( ) x
– 7

4. Factor 4x2 – 20x + 9 4 • 9 = 36 4x2 – 2x 18x – + 9 2x ( ) 2x – 1 -9
Step 1) is to re-write the MIDDLE term as TWO TERMS
1a) Multiply the First and Last Term (coefficients)
1b) Find all the factors of 36
4 • 9 = 36
1c) Find the two factors to replace the
MIDDLE TERM
1 • 36
2• 18
Step 2) Split in half
3 • 12
Step 5) Factor the first half
4 • 9
Step 6) Both halves have something in common
6 • 6
Step 7) Factor second half
Step 8) Factor the common
4x2 – 2x
18x –
+ 9 2x
( ) 2x
– 1 -9
(2x – 1)
(2x – 1)
( ) 2x –9

5. Factor 4x2 – 20x + 9 (2x – 1) ( ) 2x –9 (2x – 1)(2x – 9) First Outer
( ) 2x –9
Step 9) Check answer
(2x – 1)(2x – 9)
First
Outer
Inner
Last
4x2
-18x
-2x +9
4x2
– 20x
+ 9

6. Factor 3x2 + 22x + 7 3 • 7 = 21 3x2 + x + 21x + 7 x ( ) 3x + 1 +7
3 • 7 = 21
3x2 + x +
21x
+ 7 x
( ) 3x
+ 1 +7
(3x + 1)
1 • 21
3 • 7
(3x + 1)
( ) x
+ 7
Check answer
(3x + 1)(x + 7)
First
Outer
Inner
Last
3x2
+21x +x +7
3x2
+ 22x
+ 7

7. Factor 10x2 + 13x – 3 10 • 3 = -30 10x2 – 2x + 15x – 3 2x ( ) 5x – 1
Checkpoint
Factor
10x2
+ 13x
– 3
10 • 3 =
10x2 – 2x +
15x
– 3 2x
( ) 5x
– 1 +3
(5x – 1)
1 • 30
2 • 15
3 • 10
(5x – 1)
( ) 2x
+ 3
5 • 6
Check answer
(5x – 1)(2x + 3)
First
Outer
Inner
Last
10x2
+15x
-2x -3
10x2
+ 13x
– 3

8. Factor 9x2 + 42x – 15 3( ) 3x2 + 14x – 5 3x2 x – + 15x – 5 3 • 5 = -15
#4 Factor with a Common Factor for a, b, and c
Factor
9x2
+ 42x
– 15
3( )
3x2
+ 14x
– 5
3x2 x – +
15x
– 5
3 • 5 = x
( ) 3x
– 1 +5
(3x – 1)
1 • 15
3 • 5 3
(3x – 1)
( ) x
+ 5
Check answer
(3x – 1)(x + 5)
First
Outer
Inner
Last
3x2
+15x -x -5
3x2
+ 14x
– 5

9. Factor -12x2 + 10x + 2 -2( ) 6x2 – 5x – 1 6x2 6x – + x – 1 6 • 1 = -6
Checkpoint
Factor
-12x2
+ 10x
+ 2
-2( )
6x2
– 5x
– 1
6x2 6x – + x
– 1
6 • 1 = 6x
( ) x
– 1
+ 1
(x – 1)
1 • 6
2 • 3 -2
(x – 1)
( ) 6x
+ 1
Check answer
(x – 1)(6x + 1)
First
Outer
Inner
Last
6x2 +x
-6x -1
6x2
– 5x
– 1

10. Factor 15x2 – 35x + 10 5( ) 3x2 – 7x + 2 3x2 6x – – x + 2 3 • 2 = 6 3x
Checkpoint
Factor
15x2
– 35x
+ 10
5( )
3x2
– 7x
+ 2
3x2 6x – – x
+ 2
3 • 2 = 6 3x
( ) x
– 2 –1
(x – 2)
1 • 6
2 • 3 5
(x – 2)
( ) 3x
– 1
Check answer
(x – 2)(3x – 1)
First
Outer
Inner
Last
3x2 -x
-6x +2
3x2
– 7x
+ 2

11. Solve 6x2 + 10x + 15 = 2x2 + 26x 60 -2x2 -26x -2x2 -26x 4x2 – 16x + 15
#5 Solve a Quadratic Equation
Solve
6x x + 15 = 2x2 + 26x 60
-2x2
-26x
-2x2
-26x
1• 60
2 • 30
4x2
– 16x
+ 15 =
3 • 20
4 • 15
4x2 – 6x –
10x
+ 15
5 • 12 2x
( ) 2x
– 3
– 5
(2x – 3)
6 • 10
(2x – 3)
( ) 2x
– 5 =
2x – 3 = 0 or
2x – 5 = 0 2x = 3 2x = 5 5 x = 3 2 x = 2

12. Solve 14n2 + 10n + 2 = -17n –7 126 +17n +7 +17n +7 14n2 + 27n + 9 =
Checkpoint
Solve
14n n + 2 = -17n –7
126
+17n +7
+17n +7
1• 126
2 • 63
14n2
+ 27n
+ 9 =
3 • 42
6 • 21
14n2 + 6n +
21n
+ 9 2n
( ) 7n
+ 3 +3
(7n +3)
(7n +3)
( ) 2n
+ 3 =
7n +3 = 0 or
2n + 3 = 0 -3 -3 -3 -3 1 7n = -3 1 2n = -3 3 n = – 3 2 n = – 7

13. Assignment
Book Pg. 606 – 607
#22, 25, 27, 28, 31, 32, 42, 48, 49, 52