1. AM 1.2g To Factor Multiple Quadratics
AM 1.2g To Factor Multiple Quadratics

2. Active Learning Assignment?4

3. FACTORING RULES! 0 = ax2 + bx + c (Standard Form)
Always see if you can factor out a common term. COUNT TERMS!!!
TWO TERMS: ……
THREE TERMS: a) Single Quadratic-… b) Multiple Quadratic: Multiply the Quadratic and Constant (first and last) terms. Look to see what multiplies to give that product that combines to get the linear (middle) term. “Granny Glasses ” Replace the linear term and factor by parts.
Quadratic
Linear
Constant
0 = ax2 + bx + c
(Standard Form)

4. LESSON:
Today, we are looking at factoring when the leading coefficient is more that “1”. That is, when our polynomial looks like this: 2x2 + 7x + 6 (notice, the leading coefficient is more than “1”)
To factor, multiply the quadratic term with the constant term. Look at what multiplies to get that number that combines to get the linear term:
2x2 + 7x + 6
What multiplies to get 12x2:
12x2
= ( ) ( ) 4x 3x 7x
= ( ) + ( ) 4x 3x
That combines to get 7x:

5. x2 + 7x + 6
What multiplies to get 12x2:
12x2
= ( ) ( ) 4x 3x
Replace the middle term: 7x
= ( ) + ( ) 4x 3x
That combines to get 7x:
2x2 + 4x + 3x + 6
Now, what does this look like?
2x ( ) + 3 ( )
x + 2
x + 2
(x + 2)
(2x + 3)

6. FACTOR:
x2 + 5x + 2
4x2
= ( ) ( ) 4x 1x 5x
= ( ) + ( ) 4x
2x2 + 4x + 1x + 2 1x
2x ( ) + 1 ( )
x + 2
x + 2
(x + 2)
(2x + 1)
x2 – 4x + 1
3x2
= ( ) ( )
-3x
-1x
-4x
= ( ) + ( )
-1x
-3x
3x2 + -3x + -1x + 1
3x ( ) – 1 ( )
x – 1
x – 1
(3x – 1)
(x – 1)

7. x2 + 2x – 5
x2 + 48x – 20

8. Look at factors of 72, start with 1: Multiply Subt. 1, 72 71 2, 36 34
What if you have really big numbers?
x2 – 6x – 9
Look at factors of 72, start with 1:
Multiply Subt. 1, 2, 3, 4,
6, *

9. x2 – 12x – 5
x2 – 4x – 4

10. Do the Factor Worksheet Multiple Quadratic (E):
7, 8, , 24, , 30, 33, , 41, 51