1. Essential Question: How do I divide polynomials?
How do I perform polynomial long division?
How do I perform polynomial synthetic division?

2. The following are our current tools for solving polynomials:
Factoring
Most of the time the easiest, but only works with rational zeros.
Quadratic Formula
Works with all zeros, but can be a little messy. MUST USE for irrational & imaginary zeros.
Completing the Square
Again, same as quadratic formula.
Graphing
Can only get an approximate value of irrational zeros, and can’t find imaginary zeros.

3. Is there another way to divide polynomials??? Of course!
SYNTHETIC DIVISION
When will we use synthetic division? ONLY when the divisor is a linear binomial with a leading coefficient of 1!!!! EXS  (x + 1), (x – 3), etc.
We will take a look at synthetic division using linear binomials with coefficients other than one a little later…get excited!!

4. 𝒙 𝟑 −𝟑 𝒙 𝟐 −𝒙+𝟏+ 𝟏 𝒙+𝟑 Use Synthetic Division to divide
x4 – 10x2 – 2x by (x + 3) -3 1
-10 -2 4 -3 9 3 -3 1 -3 -1 1 1
remainder
𝒙 𝟑 −𝟑 𝒙 𝟐 −𝒙+𝟏+ 𝟏 𝒙+𝟑

5. Practice Problem

6. More Practice!!