### Dealing With IndexesIf 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(a^{n})^{m}=a^{n+m} | a^{m}/a^{n}=a^{m-n} | a^{0}=1 | a^{-n}=1/a^{n} |
### Factoring x2+bx+cFind a 2 numbers whose sum is b and products of c |
### More factoring1. 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 Factorletters: 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 FractionsSimplify 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 functionf(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 expressionsMultiplication | Factor denominator, mutliply, reduce | Divison | flip 2nd equation and multiply | Unlike denominators + & - | Factor denominator, Find LCD,simplify top |
x+2/x^{2} + x - 42 * x+7/x^{2} - 4
x+2/(x-6)(x+7) * x+7/(x-2)(x+2)
x-2/x-6
8/x-2+x - 6/x^{2}-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 notationseparate between the operation for each term then solve each, then combine |
(2x10^{3})(1.8x10^{-7})
2x1.8=3.6
10^{3}x10^{-7}=10^{-4}
**Answer:** 3.6x10^{-4} ### Special case and FACTORING | 1.(a+b)(a-b)= a^{2}-b^{2} | Perfect Square Trinomial | 2. (a+b)^{2}= a^{2}+2ab+b^{2} | 4. (a-b)^{2}= a^{2}-2ab+b^{2} | Sum & Difference of Cubes | 3.a^{3}-b^{3}= (a-b)(a^{2}+ab+b^{2} | 5.a^{3}+b^{3}= (a+b)(a^{2}-ab+b^{2} | Difference of Square | 6.(a- b)^{2}= (a-b)(a+b) |
| | ### Functionsf(x)=x+4 when x=4-> | solve by replacing the x with the one inside the f() |
### Graphingit'll ask for you to solve the equation then graph your solutions, they should be x |
### Rational equationsFactor 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 |

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