Algebra 1
Name: _______________________________
Unit 6: Lesson 7
Date: _________________ Period: _______
Factoring Polynomials Completely (10.8)
Mixed Methods
Essential Questions:
 How do you know a polynomial is factored completely?
 How do you know that a polynomial is prime?
Goal:
 Students will factor polynomials completely by choosing then using a variety of different methods.
Review of ALL Factoring Methods:
Binomials
Trinomials
4-Terms
1) GCF
1) GCF
1) GCF
2) DOTS
2) X-Method
2) Grouping
*** “Factor Completely” means always check for more
ways to factor after each step***
Section 1: Solve by “Factoring Completely”… GCF then X-Method
1) Solve:
2) Solve:
4 x3  20 x2  24 x  0
18k 3  33k 2  6k  0
Set = 0 ?
YT 1) Solve:
5 y 3  25 y 2  30 y  0
Factored?
Factored?
Check ?
Check ?
Set = 0 ?
YT 2) Solve:
48x3  72 x2  27 x  0
45r 4  20r 2
Set = 0 ?
Factored?
Factored?
Check ?
Check ?
Section 2: Factor Completely… GCF then DOTS
3) Factor:
Set = 0 ?
YT 3) Factor:
75a 6  3a 4
Section 3: Factor Completely… GCF then Grouping
3r 3  15r 2  6r  30
4) Factor:
YT 4) Factor:
12b4  10b3  48b  40
Section 4: Solve by “Factoring Completely”… Grouping then DOTS
5) Solve:
y3  6 y 2  4 y  24  0
Set = 0 ?
YT 5) Solve:
2t 3  3t 2  50t  75  0
Set = 0 ?
Factored?
Factored?
Check ?
Check ?
Section 5: Factor Completely… GCF only
6) Factor:
33x5  121x 2
YT 6) Factor:
2m2  8
YT 7) Factor:
81q 4  16
Section 6: Factor Completely… “Double” DOTS
7) Factor:
Homework:
625 p 4  1
“Factoring” Packet
# 131-140 ALL
Ticket Out/Lesson Summary: True or False.
_________ 1) A polynomial is factored completely if after doing one method, another method exists.
_________ 2) If a polynomial can be factored by GCF only, it cannot be factored completely therefore it is prime.
_________ 3) For a polynomial to be factored completely, more than one factoring method needs to be used.