Test 1- Ch. A Flashcards
determine the values that must be excluded from the domain of the variable in each expression.
whatever makes the denominator zero
determine the domain of the variable x in each expression
x can’t equal (=/) whatever would make the denominator zero
negative in parenthesis
attached to number
negative not in parenthesis
not attached to number
negative exponent
switch entire numerator and denominator
exponents (out of parenthesis) of exponents in parenthesis
multiply
exponents right out side of parenthesis
square number and multiply exponent
divide exponents
subtract them
number and letter
do not go together so only letters switch if negative exponent, numbers stay and do not go with them
add, subtract, multiply polynomials
distribute and combine like terms
how to cube polynomials
square, then do long multiplication
long division polynomials
- look at first terms outside and inside division sign
- whatever you multiply outside to get inside goes on top
- multiply that top number by every term on outside and put under values under division sign
- switch signs of what you put under
- see if first term goes into first term of remained, if not that is your remainder, if yes then do it again
Factoring remember
- GCF
2. Factor out completely
different of perfect squares
(perfect squared term x+- perfect squared term of second value)(perfect squared term x +- perfect squared term of second value)
Sum of perfect cubes
First you have simplify to what its the perfect cube of and those numbers are your a and b
a3+b3= (a+b)(a2-ab+b2)
+ - +
difference of perfect cubes
First you have simplify to what its the perfect cube of and those numbers are your a and b
a3-b3=(a-b)(a2+ab+b2)
- + +
if polynomial can’t be factored
say its prime
determine the number that should be added to complete the square of each expression then factor each expression
half of b square=number
(x+-b)^2=factored expression
synthetic division “divided by”
use opposite value
synthetic division ;x-?
use opposite value
synthetic division is a factor if
=0
simplify radical expression
factor out top and bottom and cancel out
add, subtract, multiply, divide ration expressions
- Put fractions next to each other (turn division into multiplication)
- Factor
- Cancel out
- Combine
- Simplify
as soon as possible
one fraction
solve each equation
combine like terms
- set to zero
two x’s
2 values of x
- check for extraneous solution
solving absolute value equation
make one equal to positive and one equal to negative and solve
absolute value equals negative number
no solution
(4(x-2))^x=
4x(x-2)
discriminate
b^2-4ac
if b^2-4ac>0
two unequal real solutions
if b^2-4ac=0
repeated real solution
if b^2-4ac
no real solution
