LONG DIVISION AND SYNTHETIC DIVISION

Long Division

You can use long division to factor a polynomial function and to find its zeros.

Make sure your dividend is in standard from (descending order).

You must include any missing terms using 0 as the coefficient.

Divide the dividend by the first term of the divisor.

Example:

Divide:



Insert the missing term!



Answer:

Your answer will always be the dividend divided by the divisor equal to the quotient plus the remainder divided by the divisor. So for this problem that would be:



Because the remainder is zero we know that (2x-3) is a factor of  and a zero occurs at



Here is a link to another example that is a bit more challenging:

http://www.youtube.com/watch?v=l6_ghhd7kwQ

Synthetic Division

When the divisor is in the form (x-k) another way to divide polynomials is to use synthetic division.

Synthetic cannot be used when you are dividing a polynomial by a quadratic .

Synthetic is used to factor a function and find the zeros of the polynomial.

You must include any missing terms using 0 as the coefficient.

Vertical Pattern: Add the terms
Horizontal Patern: Multiply by the zero (k)

Example:

Divide:



Insert the missing term!

Notice that the -3 out front is the opposite of the +3 from the above problem.



Remainder = 1

Answer:

Your answer will always be the dividend divided by the divisor equal to the quotient plus the remainder divided by the divisor. So for this problem that would be:



Because there is a remainder,   is not a factor of .

Here is a link to another example:
 http://www.youtube.com/watch?v=bZoMz1Cy1T4