.lst-kix_92tou2eydnyc-0 > li:before{content:"● "}.lst-kix_92tou2eydnyc-1 > li:before{content:"○ "}ol.lst-kix_ykrv90m20537-5.start{counter-reset:lst-ctn-kix_ykrv90m20537-5 0}.lst-kix_mr6wn5a51d5v-2 > li{counter-increment:lst-ctn-kix_mr6wn5a51d5v-2}.lst-kix_ykrv90m20537-6 > li{counter-increment:lst-ctn-kix_ykrv90m20537-6}.lst-kix_92tou2eydnyc-6 > li:before{content:"● "}ol.lst-kix_1f6lfdtukceq-0.start{counter-reset:lst-ctn-kix_1f6lfdtukceq-0 0}.lst-kix_mr6wn5a51d5v-1 > li{counter-increment:lst-ctn-kix_mr6wn5a51d5v-1}.lst-kix_92tou2eydnyc-4 > li:before{content:"○ "}.lst-kix_92tou2eydnyc-5 > li:before{content:"■ "}.lst-kix_92tou2eydnyc-2 > li:before{content:"■ "}.lst-kix_92tou2eydnyc-3 > li:before{content:"● "}.lst-kix_ykrv90m20537-7 > li{counter-increment:lst-ctn-kix_ykrv90m20537-7}ol.lst-kix_1f6lfdtukceq-3.start{counter-reset:lst-ctn-kix_1f6lfdtukceq-3 0}ol.lst-kix_ykrv90m20537-2.start{counter-reset:lst-ctn-kix_ykrv90m20537-2 0}.lst-kix_mr6wn5a51d5v-3 > li{counter-increment:lst-ctn-kix_mr6wn5a51d5v-3}.lst-kix_1f6lfdtukceq-0 > li{counter-increment:lst-ctn-kix_1f6lfdtukceq-0}.lst-kix_mr6wn5a51d5v-0 > li{counter-increment:lst-ctn-kix_mr6wn5a51d5v-0}ol.lst-kix_mr6wn5a51d5v-5.start{counter-reset:lst-ctn-kix_mr6wn5a51d5v-5 0}.lst-kix_ykrv90m20537-8 > li{counter-increment:lst-ctn-kix_ykrv90m20537-8}.lst-kix_ykrv90m20537-5 > li{counter-increment:lst-ctn-kix_ykrv90m20537-5}ol.lst-kix_mr6wn5a51d5v-2.start{counter-reset:lst-ctn-kix_mr6wn5a51d5v-2 0}ol.lst-kix_ykrv90m20537-0.start{counter-reset:lst-ctn-kix_ykrv90m20537-0 0}.lst-kix_ykrv90m20537-3 > li{counter-increment:lst-ctn-kix_ykrv90m20537-3}ol.lst-kix_mr6wn5a51d5v-4.start{counter-reset:lst-ctn-kix_mr6wn5a51d5v-4 0}.lst-kix_1f6lfdtukceq-7 > li{counter-increment:lst-ctn-kix_1f6lfdtukceq-7}.lst-kix_1f6lfdtukceq-1 > li{counter-increment:lst-ctn-kix_1f6lfdtukceq-1}.lst-kix_mr6wn5a51d5v-5 > li{counter-increment:lst-ctn-kix_mr6wn5a51d5v-5}ol.lst-kix_1f6lfdtukceq-6.start{counter-reset:lst-ctn-kix_1f6lfdtukceq-6 0}ol.lst-kix_ykrv90m20537-7.start{counter-reset:lst-ctn-kix_ykrv90m20537-7 0}ol.lst-kix_ykrv90m20537-1.start{counter-reset:lst-ctn-kix_ykrv90m20537-1 0}ol.lst-kix_mr6wn5a51d5v-6{list-style-type:none}ol.lst-kix_ykrv90m20537-8.start{counter-reset:lst-ctn-kix_ykrv90m20537-8 0}ol.lst-kix_mr6wn5a51d5v-7{list-style-type:none}ol.lst-kix_mr6wn5a51d5v-8{list-style-type:none}ol.lst-kix_mr6wn5a51d5v-2{list-style-type:none}ol.lst-kix_mr6wn5a51d5v-3{list-style-type:none}ol.lst-kix_1f6lfdtukceq-5.start{counter-reset:lst-ctn-kix_1f6lfdtukceq-5 0}ol.lst-kix_mr6wn5a51d5v-4{list-style-type:none}ol.lst-kix_mr6wn5a51d5v-5{list-style-type:none}ol.lst-kix_mr6wn5a51d5v-0{list-style-type:none}ol.lst-kix_mr6wn5a51d5v-1{list-style-type:none}.lst-kix_ykrv90m20537-0 > li{counter-increment:lst-ctn-kix_ykrv90m20537-0}.lst-kix_1f6lfdtukceq-4 > li{counter-increment:lst-ctn-kix_1f6lfdtukceq-4}.lst-kix_mr6wn5a51d5v-7 > li{counter-increment:lst-ctn-kix_mr6wn5a51d5v-7}.lst-kix_ykrv90m20537-1 > li{counter-increment:lst-ctn-kix_ykrv90m20537-1}.lst-kix_mr6wn5a51d5v-8 > li{counter-increment:lst-ctn-kix_mr6wn5a51d5v-8}ol.lst-kix_mr6wn5a51d5v-6.start{counter-reset:lst-ctn-kix_mr6wn5a51d5v-6 0}.lst-kix_1f6lfdtukceq-1 > li:before{content:"" counter(lst-ctn-kix_1f6lfdtukceq-1,lower-roman) ". "}ol.lst-kix_mr6wn5a51d5v-3.start{counter-reset:lst-ctn-kix_mr6wn5a51d5v-3 0}.lst-kix_1f6lfdtukceq-0 > li:before{content:"" counter(lst-ctn-kix_1f6lfdtukceq-0,lower-latin) ". "}ol.lst-kix_ykrv90m20537-6.start{counter-reset:lst-ctn-kix_ykrv90m20537-6 0}.lst-kix_1f6lfdtukceq-3 > li{counter-increment:lst-ctn-kix_1f6lfdtukceq-3}ol.lst-kix_1f6lfdtukceq-1.start{counter-reset:lst-ctn-kix_1f6lfdtukceq-1 0}.lst-kix_1f6lfdtukceq-6 > li{counter-increment:lst-ctn-kix_1f6lfdtukceq-6}ol.lst-kix_ykrv90m20537-3.start{counter-reset:lst-ctn-kix_ykrv90m20537-3 0}ol.lst-kix_ykrv90m20537-8{list-style-type:none}ol.lst-kix_ykrv90m20537-6{list-style-type:none}ol.lst-kix_ykrv90m20537-7{list-style-type:none}ol.lst-kix_ykrv90m20537-4{list-style-type:none}ol.lst-kix_1f6lfdtukceq-4.start{counter-reset:lst-ctn-kix_1f6lfdtukceq-4 0}ol.lst-kix_ykrv90m20537-5{list-style-type:none}ol.lst-kix_ykrv90m20537-2{list-style-type:none}.lst-kix_ykrv90m20537-2 > li{counter-increment:lst-ctn-kix_ykrv90m20537-2}ol.lst-kix_1f6lfdtukceq-7.start{counter-reset:lst-ctn-kix_1f6lfdtukceq-7 0}ol.lst-kix_ykrv90m20537-3{list-style-type:none}ol.lst-kix_ykrv90m20537-0{list-style-type:none}ol.lst-kix_ykrv90m20537-1{list-style-type:none}.lst-kix_mr6wn5a51d5v-6 > li{counter-increment:lst-ctn-kix_mr6wn5a51d5v-6}.lst-kix_mr6wn5a51d5v-2 > li:before{content:"" counter(lst-ctn-kix_mr6wn5a51d5v-2,lower-roman) ". "}.lst-kix_mr6wn5a51d5v-1 > li:before{content:"" counter(lst-ctn-kix_mr6wn5a51d5v-1,lower-latin) ". "}.lst-kix_mr6wn5a51d5v-3 > li:before{content:"" counter(lst-ctn-kix_mr6wn5a51d5v-3,decimal) ". "}ul.lst-kix_92tou2eydnyc-8{list-style-type:none}.lst-kix_mr6wn5a51d5v-0 > li:before{content:"" counter(lst-ctn-kix_mr6wn5a51d5v-0,decimal) ". "}.lst-kix_mr6wn5a51d5v-4 > li:before{content:"" counter(lst-ctn-kix_mr6wn5a51d5v-4,lower-latin) ". "}ol.lst-kix_1f6lfdtukceq-2.start{counter-reset:lst-ctn-kix_1f6lfdtukceq-2 0}ol.lst-kix_mr6wn5a51d5v-1.start{counter-reset:lst-ctn-kix_mr6wn5a51d5v-1 0}ol.lst-kix_1f6lfdtukceq-0{list-style-type:none}.lst-kix_ykrv90m20537-6 > li:before{content:"" counter(lst-ctn-kix_ykrv90m20537-6,decimal) ". "}.lst-kix_ykrv90m20537-4 > li{counter-increment:lst-ctn-kix_ykrv90m20537-4}.lst-kix_mr6wn5a51d5v-8 > li:before{content:"" counter(lst-ctn-kix_mr6wn5a51d5v-8,lower-roman) ". "}.lst-kix_mr6wn5a51d5v-4 > li{counter-increment:lst-ctn-kix_mr6wn5a51d5v-4}.lst-kix_ykrv90m20537-7 > li:before{content:"" counter(lst-ctn-kix_ykrv90m20537-7,lower-latin) ". "}ol.lst-kix_mr6wn5a51d5v-8.start{counter-reset:lst-ctn-kix_mr6wn5a51d5v-8 0}ol.lst-kix_1f6lfdtukceq-5{list-style-type:none}.lst-kix_mr6wn5a51d5v-6 > li:before{content:"" counter(lst-ctn-kix_mr6wn5a51d5v-6,decimal) ". "}ol.lst-kix_1f6lfdtukceq-6{list-style-type:none}ol.lst-kix_1f6lfdtukceq-7{list-style-type:none}.lst-kix_mr6wn5a51d5v-5 > li:before{content:"" counter(lst-ctn-kix_mr6wn5a51d5v-5,lower-roman) ". "}.lst-kix_mr6wn5a51d5v-7 > li:before{content:"" counter(lst-ctn-kix_mr6wn5a51d5v-7,lower-latin) ". "}ol.lst-kix_1f6lfdtukceq-8{list-style-type:none}.lst-kix_ykrv90m20537-8 > li:before{content:"" counter(lst-ctn-kix_ykrv90m20537-8,lower-roman) ". "}ol.lst-kix_1f6lfdtukceq-1{list-style-type:none}ol.lst-kix_1f6lfdtukceq-2{list-style-type:none}ol.lst-kix_1f6lfdtukceq-3{list-style-type:none}ol.lst-kix_1f6lfdtukceq-4{list-style-type:none}ol.lst-kix_1f6lfdtukceq-8.start{counter-reset:lst-ctn-kix_1f6lfdtukceq-8 0}.lst-kix_1f6lfdtukceq-2 > li:before{content:"" counter(lst-ctn-kix_1f6lfdtukceq-2,decimal) ". "}ol.lst-kix_mr6wn5a51d5v-0.start{counter-reset:lst-ctn-kix_mr6wn5a51d5v-0 0}.lst-kix_1f6lfdtukceq-3 > li:before{content:"" counter(lst-ctn-kix_1f6lfdtukceq-3,lower-latin) ". "}.lst-kix_1f6lfdtukceq-4 > li:before{content:"" counter(lst-ctn-kix_1f6lfdtukceq-4,lower-roman) ". "}ol.lst-kix_ykrv90m20537-4.start{counter-reset:lst-ctn-kix_ykrv90m20537-4 0}.lst-kix_ykrv90m20537-5 > li:before{content:"" counter(lst-ctn-kix_ykrv90m20537-5,lower-roman) ". "}.lst-kix_1f6lfdtukceq-5 > li{counter-increment:lst-ctn-kix_1f6lfdtukceq-5}.lst-kix_1f6lfdtukceq-6 > li:before{content:"" counter(lst-ctn-kix_1f6lfdtukceq-6,lower-latin) ". "}.lst-kix_1f6lfdtukceq-2 > li{counter-increment:lst-ctn-kix_1f6lfdtukceq-2}.lst-kix_92tou2eydnyc-7 > li:before{content:"○ "}.lst-kix_1f6lfdtukceq-5 > li:before{content:"" counter(lst-ctn-kix_1f6lfdtukceq-5,decimal) ". "}.lst-kix_ykrv90m20537-4 > li:before{content:"" counter(lst-ctn-kix_ykrv90m20537-4,lower-latin) ". "}.lst-kix_92tou2eydnyc-8 > li:before{content:"■ "}.lst-kix_1f6lfdtukceq-8 > li{counter-increment:lst-ctn-kix_1f6lfdtukceq-8}.lst-kix_ykrv90m20537-3 > li:before{content:"" counter(lst-ctn-kix_ykrv90m20537-3,decimal) ". "}ul.lst-kix_92tou2eydnyc-4{list-style-type:none}ul.lst-kix_92tou2eydnyc-5{list-style-type:none}ul.lst-kix_92tou2eydnyc-6{list-style-type:none}.lst-kix_ykrv90m20537-0 > li:before{content:"" counter(lst-ctn-kix_ykrv90m20537-0,decimal) ". "}.lst-kix_ykrv90m20537-2 > li:before{content:"" counter(lst-ctn-kix_ykrv90m20537-2,lower-roman) ". "}ul.lst-kix_92tou2eydnyc-7{list-style-type:none}ul.lst-kix_92tou2eydnyc-0{list-style-type:none}.lst-kix_1f6lfdtukceq-7 > li:before{content:"" counter(lst-ctn-kix_1f6lfdtukceq-7,lower-roman) ". "}.lst-kix_1f6lfdtukceq-8 > li:before{content:"" counter(lst-ctn-kix_1f6lfdtukceq-8,decimal) ". "}ul.lst-kix_92tou2eydnyc-1{list-style-type:none}ul.lst-kix_92tou2eydnyc-2{list-style-type:none}ol.lst-kix_mr6wn5a51d5v-7.start{counter-reset:lst-ctn-kix_mr6wn5a51d5v-7 0}.lst-kix_ykrv90m20537-1 > li:before{content:"" counter(lst-ctn-kix_ykrv90m20537-1,lower-latin) ". "}ul.lst-kix_92tou2eydnyc-3{list-style-type:none}
In general f, g are polynomials
- Degree of f
degree of g
ie
must do polynomial divisionDon't forget about the age old question of What are the layers of the Earth?
If you want to learn more check out What happens to price and quantity of golf club membership as wealth increases?
- Distinct Factors

- Repeated factors
Don't forget about the age old question of What are the regulatory mechanisms?
- Irreducible Factor

If you want to learn more check out What does range measure?
Don't forget about the age old question of What is a political ideology?
7.5 Partial Fractions
Question 1. True or False? 
If you want to learn more check out Discuss the two major periods for the cell.

Question 2. The first step in any partial fraction problem is to factor the denominator. Consider the rational expression (x-4)(x+2)


If we factor the denominator, then we find that





Question 3. Which method will be most efficient in solving the integral 

Substitution =
In general f, g are polynomials
Degree of f
degree of g 
ie.
must do a polynomial division
Question4. How can we integrate 

Question 5. Setup the partial fraction decomposition for:
-

When x = -2 -2= 0 + 0 +- 8C = C =¼
When x = 6 6= 64A + 0 + 0 = A = 3/32
When x = 0 4A 4a - 12B -6C = B =
To solve:
- multiply time common denom.
- Plug in #s for x, good choices would com from common denom





Question 6. Bonus question! True or false? 