Factors and zero's are connected by the fact that if you have a factor you can easily find the zero's and if you have a zero you can find the factor of a function. You can find a zero from a factor by setting the factor equal to zero and solving for the missing value. (see below)
x+2 = 0 x = -2 | On the left shows how to get a zero from a factor and on the right is the reverse, showing how to get a factor from a zero. | x = -2 x+2 = 0 (x+2) = 0 |
Division helps us determine what the factors are for the function. Since polynomials can get fairly complicated we can't simply factor out the x's, so we use division to simplify the process. Division helps you find all of the factors and whether or not a particular factor actually does work. If there is a remainder then it is not a factor. To start off your division you need a factor which you can find by graphing your polynomial. Any zero's that you find can be turn into a factor and used for division.