1. Algebra
Factoring Completely

2. Steps to Factor Completely
Factor out the GCF (Greatest Common Factor)
Look for Special Patterns
DTS a²- b²
PST a²+ 2ab + b²
a² - 2ab + b²
3. Factor ax² + bx + c
4. If 4 terms, try FACTOR BY GROUPING
5. Check that each factor is prime
6. FOIL to check
7. If part of an equation, solve using the ZERO PRODUCT PROPERTY
(a + b)(a – b)
(a + b)²
(a - b)²

3. Greatest Common Factor (GCF)
A term that combines the GCF of the coefficients with the lowest power of the variable.
Polynomial
GCF
Factored
9x²- 15x 3x
3x(3x – 5)
14x³- 21x2
7x²
7x²(2x – 3)
2x²- 8 2
2(x²- 4)
DTS!
2(x + 2)(x – 2)
3(x²+ 6x + 9)
3x²+ 18x + 27 3
PST!
3(x + 3)²

4. Factor! 4x³- 36x 4x(x + 3)(x – 3) 4x(x²- 9) 5n²(3n + 2)(3n – 2)
DTS!
5n²(3n + 2)(3n – 2)
45n4- 20n2
5n²(9n²- 4)
DTS!
4a(a + 2)(a + 3)
4a³+ 20a² + 24a
4a(a²+ 5a + 6)
7x³- 7x²- 84x
7x(x + 3)(x – 4)
7x(x²- x - 12)

5. Solve! 2x³- 10x²+ 8x = 0 2x(x – 4)(x– 1) = 0 2x(x²- 5x + 4) = 0
16y³- 100y = 0
4y(2y + 5)(2y – 5) = 0
4y(4y²- 25)
DTS!
y = 0, -5/2, 5/2
3x²- 30x + 75 = 0
3(x – 5)² = 0
3(x²- 10x + 25) = 0
x = 5
PST!

6. Factor by Grouping (4 terms)
x³+ 2x²+ 3x + 6
Divide into 2 parts
LEFT side, RIGHT side
GCF is x²
GCF is 3
Each side has a GCF
same
same x²
(x + 2) (x + 2)
+ 3
FACTOR each side
FOIL to check
( )
(x + 2)
x³+ 2x²+ 3x + 6
Check!

7. Factor! x³- 2x²- 9x + 18 x² (x – 2) - 9 (x – 2) (x²- 9) (x – 2)
DTS!
x³- 3x²+ x - 3 x²
(x – 3)
+ 1
(x – 3)
(x²+ 1)
(x – 3)
(x²+ 1)(x – 3)

8. A Few from the HW
P 629 # 19 and # 34

9. Homework
pg #19-35 odd
pg Quiz 3 #1-25