How do we multiply rational expressions ?

Multiplying rational expressions is similar to dividing polynomials. All you have to do is factor and eliminate the terms. Here is an example to help you out :

X²+8x+15             (X+5) (X+3)        ( X+3)

                   • =                      =                                                                   

X²+10x+25            (X+5) (X+5)         ( X+5) 

If you are having any trouble look at the picture , it might help you out : 

                    

How do we divide polynomials ?

A polynomial is an mathematical expression with terms and constants. Follow these steps if you want to learn how to divide a polynomial : 

Step 1 : if not factored already , factor your expression .

Step 2 : Eliminate similar  terms . ( EX. ( 2x-6) and ( 2x-6) these will cancel out because they are alike.) 

DONE ! 

Example : 

(X²+2x+1)        (X+1) (X+1)

                    =                       

    (X+1)                    (X+1)

Final Answer : ( X+1)

How Do We Solve Diamond Problems ?

Diamond Problems :

A diamond problem is a X shaped problem where  you have to find two digits that both have a sum of the number on the top of the X and a product of the number on the bottom of the X to find the left and right digits.

     *

  \ A /                             
?  X  ?                
  / B \
    +

For an example , 

     *

  \ 12 /                             
?  X  ?                
  / 7 \
    +

To find the solution you have to find the factors of 12 you could list them if it helps you . Now match it up to see which numbers that sum up to 7 . Your final results would be  3 and 4 .

How Do We Multiply Binomials ?

To multiply binomials you need to use the FOIL Method.


FOIL abbriviate:


First
Outer
Inner
Last


Here is an example :


(8x+9)(2x+5)


Step 1 :First: you have to multiply 8x with 2x which equals to 16x^2


Step 2 : Outer: You have to multuiply 8x with 5 which is going to equal to 40x


Step 3 : Inner : You have to multiply 9 with 2x which gives you 18x.


Step 4 : Last : you have to find the product of 9 and 5 which is 45.


Step 5 : Combine the like terms , in this case it is 40x and 18x . After combineing the terms you should get 58x.


Step 6 : Put the solution in standard form :
16x^2+58x+45 , and thats it youre DONE ! :)

How do we classify polynomials ?

You can classify a polynomial based on its degree and number of terms.