Dividing Polynomials (synthetic division and long division)

Synthetic Division

1. Place the coefficients in descending order on inside

2. Place number (possible zero or the zero given) on the outside

pay attention- if there is a missing term don't skip it replace it with zero... 

final answer written as 

 

If you are not given the number(possible zero) to divide by, then you must find the possible numbers yourself.

To find this zero you take the factors of the last term, the constant, and divide them by the factors of the first term, the leading coefficient. (rational root theorem)

 Factor out an x 

x=0

 a shortcut to find a zero: when all the coefficients add to zero, the zero is 1.If this does not work then it is pretty much trial and error based off of the rational root theorem

 x=1

x=1 again

now you are left with 

which can be factored to

x=1, x= -2

the zeros altogether are x=1 mult. of 3 and x= -2

Long Division:

final answer written as...

*synthetic division is when you are dividing by a first degree polynomial and long division can be used for a first degree or any higher degree*

videos that might help:
synthetic division-
http://www.youtube.com/watch?v=bZoMz1Cy1T4
http://www.youtube.com/watch?v=1byR9UEQJN0

long division-
http://www.youtube.com/watch?v=l6_ghhd7kwQ
http://www.youtube.com/watch?v=ok4k6HDCuIk