9-1 Factors and Greatest Common Factors
A. Definitions
1. Factors – two numbers that multiply to give you
the product.
Ex 1: find the factors of 48
2. Prime numbers – whole number whose only
factors are 1 and itself.
Ex 2: is 23 prime?
3. Composite numbers – Whole number that is not
prime.
Ex 3: Find the prime factorization of 150.
4. Prime factors - when a whole number is expressed
as the product of factors that are all prime.
Ex 4: find the prime factorization of the following.
a.) 84
b.) -132
5. Greatest common factor – the greatest number that
is a factor of two integers.
Ex 5: What is the greatest common factor of:
a.) 84 and 70?
b.) 27a 2b and 15ab 2 c
HW: Algebra 9-1 p. 477-479
21-27 odd, 30-31, 33-61 odd, 70-71, 72-86
9-2 Factoring Using the Distributive Property
A. Factoring
1. Regular
3 x 2 + 75 x can be factored to 3 x( x + 25) by doing
the reverse of distribution.
Ex 1: Factor by distribution each polynomial
a.)
b.)
c.)
d.)
12mn 2 − 18m 2 n 2 =
6 x 2 + 12 x =
28a 2b + 56abc 2
20abc + 15a 2 c − 5ac
2. Also you can do the reverse of FOILing, called
factoring by grouping.
Ex 2: Factor
a.) 5 y 2 − 15 y + 4 y − 12
b.) 20ab − 35b + 36a − 63
c.) 3 x3 + 2 xy − 15 x 2 − 10 y
d.) a 2 − ab − 7b + 7a
e.) 3a 2 − 2ab + 10b − 15a
B. Solving Equations
1. If two things multiplied together equal zero, one
of them has to be zero. ab = 0
Ex 3: solve
a.) ( x − 2)(4 x − 1) = 0
b.) 12 y 2 = 4 y
HW: Algebra 9-2 p. 484-486
17-39 odd, 44, 46, 49-59 odd, 64-74, 76-81
9-3 Factoring Trinomials
A. Factoring
1. To factor trinomials, you do the reverse of
FOILing, sometimes you may have to try a few
different ways.
Ex 1: Factor the following
a.) ( x 2 + 7 x + 10)
b.) ( x 2 − 12 x + 27 )
c.) ( y 2 + 3 y − 18 )
d.) ( a 2 − a − 6)
e.) ( x 2 − 2 x − 48)
B. Solving equations by Factoring
1. Get everything over to one side, factor and then
solve each part.
Ex 2: solve x 2 + 2 x = 15
HW: Algebra 9-3 p. 493-494
17-34, 37-53 odd, 54, 64-65, 70-76, 78-83
9-4 Factoring Trinomials ax 2 + bx + c = 0
A. Factoring
1. First put what two things multiply to give you
ax 2 .
2. Then put what two things multiply to give
you
c.
Example 1: Factor
a.) 5 x 2 + 27 x + 10
b.) 7 x 2 + 22 x + 3
c.) 2 x 2 + 9 x + 9
d.) 24 x 2 − 22 x + 3
e.) 4 x 2 + 24 x + 32
B. Solve equations by Factoring
Example 2: Solve
a.) 3 x 2 + 13 x − 10 = 0
b.) 18b 2 − 19b − 8 = 3b 2 − 5b
HW: Algebra 9-4 p. 499-500
14-30, 32-33, 35-47 odd, 54-70
9-5 Factoring Difference of Squares
A. Factor a 2 − b 2
1. Foil ( x − 7)( x + 7)
2. When you need to factor something that looks
like a 2 − b 2 , it factors to a difference of squares.
Ex 1: Factor
a.) m 2 − 64
b.) 3b3 − 27b
c.) (2 x 4 − 32)
d.) 6 x 3 + 30 x 2 − 24 x − 120
B. Solve equations by factoring
Ex 2: Solve each equation
a.) x 2 = 25
4
b.) r −
=0
25
2
c.) 48 y 3 = 3 y
HW: Algebra 9-5 p. 505-506
16-32, 34-44, 53-70