How Do We Divide Polynomials

this is the long division method 

Dividing polynomials is very easy
take a simply problem like (x+2x+1)/(x+1)
the diamond method will be helpful here.
take x+2x+1 and make the diamond

1. place the two on the top and the 1 on the bottom  
2. figure out what to numbers multiply to 1 and add up to 2
   after we find that 1 and 1 add up to 2 and multiplied to 1
3. now we replace the 2 with two 1's
   so we get (x+1x+1x+1)/(x+1)or (x+1)(x+1)/(x+1)
4. now we cancel out (x+1)/(x+1)= 1
5. so the final answer is  (x+1)/1 which equals  x+1

hoe this has helped for more help check out the link below:

• http://www.purplemath.com/modules/polydiv.htm
•  http://www.purplemath.com/modules/polydiv2.htm
•  http://www.purplemath.com/modules/polydiv3.htm
•  http://www.youtube.com/watch?v=qd-T-dTtnX4

How Do We Factor Trinomial

their is an easy way to to factor trinomials using the diamond method. For example take this trinomial : x^2+10x+25 this problem may look hard but when using the diamond method it becomes very easy.

• We first set up the diamond with 10x on the top and 25 on the bottom. 
• Now we need to find out what two numbers multiply to 25 and add to 10.
• 1 * 25 = 25 but when added 1 + 25 = 26
  5 * 5 = 25 and 5 + 5 = 10.
• Now that we found the two numbers we can now find the answer.
• We can do it the longer way which is x^2 + 5x + 5x + 25
  what dose x^2 +5x have in common one x so we get x(x+5)
  now the same thing with (5x +25) we get 5(x+5) and our final answer is (x+5)(x+5).
• and the shorter way we square root x^2 which is (x+ ) (x+ ) and then we place the two 5's which gives us the same as the longer way which is (x+5) (x+5) 

for more help click on the link below
http://www.youtube.com/watch?v=vVWm2gyROQQ&feature=fvwp&NR=1

How do we multiply binomials

there is one good method to multiply binomials it called F.O.I.L with stand for

• F.irst

• O.uter

• I.nner

• L.ast

for example
(x+3)(x+2)

1. we do the first letter in F.O.I.L. which is first we multiply (x * x) this will give us x^2
2. then we do then next letter which is O.uter we multiply (x * 2) this gives us 2x
3. next we do I.nner we multiply (3 * x) it gives us 3x
4. finally we do L.ast we will multiply (3 * 2) this gives us 6
5. now we got to combine like terms 2x+3x to get 5x  
6. our final answer is x^2+5x+6

link for more help or other methods
http://regentsprep.org/Regents/math/ALGEBRA/AV3/Smul_bin.htm

how do we solve diamond problems

When we have a problem like

ex.// 

x^2-2x-99

1. we have to make a lager X
2. then place the two numbers (-2, -99)
3. then place it in the X 
4. place the -2 on the top of the X and the -99 on the bottom
5. we have to find out what two numbers add to -2 and multiply to -99
6. we list all the multiply of -99 which are (1,-99),(3-33),(9,-11),(11,-9),(33,-3),(99,-1)
7. now we got to add them to find which will equal -2
8. after that the two number placement doesn't matter 

this is another example

how do we classify polynomials?

Ploynomial - is a monomial or the sum or diffrence ot two or more monomial

Monomial - is a expression that is a number a variable or a product of a number and one or more variables

ex .//

1. 7x/2 degree : 1
2. 3x^2y^3 degree : 5
3. -4 degree : 0
4. 9x^0 degree :0