Ok so this is Jessica blogging tonight.  I'm not very good at explaining things so hopefully you were all listening to Mr.P today.  

Today we reviewed factoring!  How exciting! 

A good thing to remember when factoring is to look for the greatest common factor. 

For example in the equation:

36xy+72x-18

The GCF would be 18 since they are all divisible by 18.

18(2xy+4x-1)

We also learned factoring by grouping.   Grouping is helpful when you have an equation like this, 9x+9y + zx+zy.  Since there isn't a common factor for all of them grouping is a good way to factor this equation.
You group the equations into two groups.  The ones that share a GCF go together.
9x+9y     +      zx+zy    
So now you factor each by the GCF
9(x+y)    +    z(x+y)
Because they both have  (x+y) the equation can be changed to:
(x+y) (9+z)

Some of the formulas that will help a lot with the next part are:
x2-y2=(x+y)(x-y) For factoring the difference of two squares.
x3-y3=(x-y)(x2+xy+y2) For factoring the difference of cubes.
x3+y3=(x+y)(x2-xy+y2) For factoring the sum of cubes.

To factor you just plug in the numbers.
Example:
36x2-64
x would be 6x and y would be 8. So you plug the numbers into the formula and bam! An answer!
(6x)2-(8)2=(6x+8) (6x-8)
To check if it's right you would just foil it out.
36x2-48x+48x-64 or 36x2-64

When you are factoring perfect square Trinomials you use the formula
x2+2xy+y2=(x+y)2 or  x2-2xy+y2=(x-y)2

The x and y values would be the same as before.

When factoring trinomials that have the form of x2+bx+c the most important thing to remember is
1. uv=c and
2.u+v=b

So say you have x2+3x-10,  if you remember the 2 rules then you know that you have to find two multiples of -10 that will add up to 3.  It's pretty easy to figure out that only 5 and -2 fit those both of the rules.
The answer would then be (x+5) (x-2)

Some more rules that can help are
1.When c is positive when u and v have the same sign, they will both have the same sign as b.  So if b is positive so are u and v and if b is negative so is u and v.   and
2.If c is negative u and v have oposite signs.

When factoring trinomials with the form ax2+bx+c with a being a number other than 1.

The rules for this are
1.df=a
2.eg=c and
3.dg+ef=b

The steps you use to solve are
1.Figure out which is a.b and c
2.Find u and v so that uv=ac and u+v=b.  and
3.Rewrite the equation and factor it by grouping.

Example:
2x2+13x+15
a=2 b=13 c=15
uv=30
u+v=13
3 and 10 both work so we change the equation to
2x2+3x+10x+15  then we solve
x(2x+3) 5(2x+3)
(2x+3) (5+x)

Long Division
The next thing we did was we reviewed long division!

Let's just do a simple long division question to jog our memories.

     948814
6/5693485     
   54                     the basic idea is to start on the left and work to the right figuring out how many times 
     29                   6 can go into each number, subtracting that and moving to the next number. 
     24                   the answer is 948814+(1/6)  
       53
       48
         54
         54
           085
             84
               R1


There are 4 steps to long division thats ridiculous like  x3+4x2+5x+2 divided by x+2.
1. Rewrite the variables in descending order.
2. Divide the first term by the first term of the divisor to get the first term of the quotient.
3. Multiply the divisor by the new term and subtract it from the new divided. (like before finding how many times the divisor can fit into the divided)
4. Repeat the new steps until the end of the question.

Example:
        x2+2x+1
 x+2/x3+4x2+5x+2
      -x3+2x2
         0+2x2 +5x
            2x2+4x
            0+1x +2
                   x+2
                       0

If we factored the equation it would be
(x+1) (x+1)
Which would be your x-intercepts if you graphed them.

That's all I got so goodnight!