### Dividing Polynomials

```Dividing Polynomials
Warm Up
Find all zeros for the following polynomials using factoring methods. Then provide a rough sketch of the polynomial. 1. 𝑓 𝑥 = 𝑥 ! + 12𝑥 ! − 64 2. 𝑓 𝑥 = 𝑥 ! + 5𝑥 ! − 36𝑥 Why divide?
Attempt to find all the exact zeros of the following function. 𝑓 𝑥 = 𝑥 ! + 4𝑥 ! + 2𝑥 + 8 Why will we need to learn how to divide monomials? Method 1 - Polynomial Long Division
Example 1: Find the quotient: (2𝑥 ! − 3𝑥 − 20) ÷ (2𝑥 + 5) Quotient: f(x) = ! ! !!! ! !!!!!
Example 2: Find the quotient: !!!
Quotient: f(x) = Example 2: Find the quotient: (3𝑥 ! + 4𝑥 ! + 8) ÷ (𝑥 + 2) Quotient: f(x) = Quotient: f(x) = Quotient: f(x) = Method 2 - Synthetic Division
Example 1: Find the quotient: (𝑥 ! + 2𝑥 ! − 5𝑥 + 16) ÷ (𝑥 − 4) !! ! !!! ! !!! ! !!!!!
Example 3: Find the quotient: !!!!
What’s the significance of the remainder?
Determine whether (𝑥 − 5) a factor of the following: a. 2𝑥 ! − 13𝑥 + 15 b. 4𝑥 ! − 11𝑥 − 3 DIVISION SCAVENGER HUNT:
Practice!
Divide the following polynomials. Rewrite the dividend as a product. State whether the divisor was a factor. ```