Math M03 Quiz #2 Cheat Sheet

A Education › Mathematics cheat sheet in English by Berger42

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Exponents

(aⁿ)^m=a^n+m	a^m/aⁿ=a^m-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.

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

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

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 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

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

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