Cheatography

# Math M03 Quiz #2 Cheat Sheet by Berger42

### Dealing With Indexes

 If Odd then nothing happens If Even then use absolute value bars If term power is even and index is odd then use absolute bars if answer is negative
Put absolute value bars on variables

### Exponents

 (an)­m­=an+m am/a­n­=am-n a0=1 a-n=­1/an

### FOIL Method ### Factoring x2+bx+c

 Find a 2 numbers whose sum is b and products of c

### More factoring

 1. 3xy-4x­-12y+16 2. x(3y-4) 4(3y-4) 3.(3y-­4)(x-4)
*Between 1&2: factor first 2 terms and last 2 terms separately
Between 2&3: remove the numbers on the outside and put them in parent­hesis

### Greatest common Factor

 letters: each term has to have one Numbers: the highest number all of terms can multiply into letter­s:Chose the one with the lowest exponent

### Complex Fractions

 Simplify the numerator and the denomi­nator of the complex fraction so that each is a single fraction. Perform the indicated division by multip­lying the numerator of the complex fraction by the reciprocal of the denomi­nator of the complex fraction. Simplify if possible.

### Rational function

 f(x)=p­(x)­/q(x) Solve it like a function
Finding domain:
Demoni­nator=0
Solve
Those values are the excluded values
Solve the rest of the equation
if you get the excluded value your answer is no real solution

### Rational expres­sions

 Multip­lic­ation Factor denomi­nator, mutliply, reduce Divison flip 2nd equation and multiply Unlike denomi­nators + & - Factor denomi­nator, Find LCD,si­mplify top
x+2/x2 + x - 42 * x+7/x2 - 4

x+2/(x­-6)­(x+7) * x+7/(x­-2)­(x+2)
x-2/x-6

8/x-2+x - 6/x2­-4+­2/x+2

8/x-2+x - 6/(x+2­)(x­-2)­+2/x+2

8+x-6+2
x-16

### Solving with Scientific notation

 separate between the operation for each term then solve each, then combine
(2x10­3)­(1.8­x1­0-7)

2x1.8=3.6

103x­10­-7­=10-4
Answ­er: 3.6x10-4

### Special case and FACTORING

 1.(a+b­)(a-b)= a2-b2 Perfect Square Trinomial 2. (a+b)2= a2+2­ab+b2 4. (a-b)2= a2-2­ab+b2 Sum & Difference of Cubes 3.a3­-b3= (a-b)(­a2­+a­b+b2 5.a3­+b3= (a+b)(­a2­-a­b+b2 Difference of Square 6.(a- b)2= (a-b)(a+b)

### Equations And Graphs ### Equations and Graphs 2 ### MORE Factoring ### Functions

 f(x)=x+4 when x=4-> solve by replacing the x with the one inside the f()

### Graphing

 it'll ask for you to solve the equation then graph your solutions, they should be x

### Rational equations

 Factor Denomi­nators find excluded values Find LCD of all terms multiply by LCD check solution
*always have at least 1 fraction

### Solving f(x) Replace the x in the equation (next to the letter) with the equation that comes after the equal sign

### Factoring Trinomials ### Factoring trinomials 2 