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Math M03 Quiz #2 Cheat Sheet by

math     what     college

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

(anm­=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)(­a+a­b+b2
5.a3­+b3= (a+b)(­a-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

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