12/4/12 how do we rationalize a denominator?

How do we rationalize a denominator?

There are two different ways you can rationalize a denominator , first understand that you can never have a radical as a square root for example : 5 over radical 9

- in order to solve this you would have to simplify the bottom by finding the square root so this becomes 5/3

Then you might come to more complex problems like 5/3+(rad.)2
the way you would solve this problem is by using the complex conjugate of the denominator so you would have (3+(rad)2)(3-(rad)2) then FOIL this
the foiled product would be ; 9-3(rad)2+3(rad)2-(rad)4 , next you need to combine like terms and the final product 11
Now you need to multiple the same number on the bottom to the top so it would be (5)(3-(rad.)2)
 this results to 15-5(rad)2/11 as the final product

11/28/12 how do we factor by grouping ?

How do we factor by grouping ?

- When you factor your taking out common terms so you need to group them , for example :
x^3+3x^2-4x-12
First factor the first half of the equation : x^3+3x^2
this becomes : x^2(x+3) because you take out the common factor and make it so that if you foil it you get what the original half of the equation was.
Second ,now you do the same thing to the other half of the equation: 4x-12
this becomes 4(x+3) because four can come out of each term
Third , you can now combine like terms (x^2 +4) (x+3)
but one of the terms can be simplified still so;
 The final equation becomes (x+2)(x+2)(x+3)

absolute value inequalities 9/13/12

How do we solve absolute value inequalities ?

-The purpose of absolute value is to change negative numbers to postive numbers
-When applying absolute value to inequalites you will have 2 'x' values representing the absolute value Example:
solve for 'x"1st:  l 5x-7 l>8
add 7 to both sides : l 5x l >15
then divide 5 from both sides to isolate the x :
l x l>3
Now you need to flip the signs:
 l 5x-7 l<-8
add 7 to both sides:
l 5x l <-1
now divide 5 from both sides to isolate 'x'
l x l <-1
Your results are :
l x l <-1
l x l <-8