Transcript 10.8 Factoring Completely

Algebra
10.8
Factoring Completely
Steps to Factor Completely
1.
2.
3.
4.
5.
6.
7.
Factor out the GCF (Greatest Common Factor)
Look for Special Patterns
DTS a²- b²
(a + b)(a – b)
(a + b)²
PST a²+ 2ab + b²
a² - 2ab + b²
(a - b)²
Factor ax² + bx + c
If 4 terms, try FACTOR BY GROUPING
Check that each factor is prime
FOIL to check
If part of an equation, solve using the
ZERO PRODUCT PROPERTY
Greatest Common Factor (GCF)
A term that combines the GCF of the coefficients
with the lowest power of the variable.
Polynomial
GCF
9x²- 15x
3x
3x(3x – 5)
14x³- 21x2
7x²
7x²(2x – 3)
2x²- 8
2
3x²+ 18x + 27
3
Factored
2(x²- 4) DTS!
2(x + 2)(x – 2)
3(x²+ 6x + 9)
3(x + 3)²
PST!
Factor!
4x³- 36x
4x(x²- 9)
4x(x + 3)(x – 3)
DTS!
45n4- 20n2
5n²(9n²- 4)
5n²(3n + 2)(3n – 2)
DTS!
4a³+ 20a² + 24a
4a(a²+ 5a + 6)
4a(a + 2)(a + 3)
7x³- 7x²- 84x
7x(x²- x - 12)
7x(x + 3)(x – 4)
Solve!
2x³- 10x²+ 8x = 0
2x(x²- 5x + 4) = 0
16y³- 100y = 0
4y(4y²- 25) DTS!
2x(x – 4)(x– 1) = 0
x = 0, 4, 1
4y(2y + 5)(2y – 5) = 0
3x²- 30x + 75 = 0
3(x²- 10x + 25) = 0
PST!
y = 0, -5/2, 5/2
3(x – 5)² = 0
x= 5
Factor by Grouping (4 terms)
x³+ 2x²+ 3x + 6
GCF is x²
GCF is 3
same
same
x²(x + 2) + 3 (x + 2)
(
) (x + 2)
x³+ 2x²+ 3x + 6
Divide into 2 parts
LEFT side, RIGHT side
Each side has a GCF
FACTOR each side
FOIL to check
Check!
Factor!
x³- 2x²- 9x + 18
x² (x – 2) - 9 (x – 2)
(x²- 9) (x – 2)
DTS!
(x + 3)(x – 3)(x – 2)
x³- 3x²+ x - 3
x² (x – 3) + 1 (x – 3)
(x²+ 1) (x – 3)
(x²+ 1)(x – 3)
A Few from the HW
• P 629 # 19 and # 34
Homework
pg. 629 #19-35 odd
pg. 632 Quiz 3 #1-25