1. 2.3 Notes: Polynomial and Synthetic Division
Date:
2.3 Notes: Polynomial and Synthetic Division
Lesson Objective: Use long and synthetic division and the Remainder and Factor Theorems to find zeros of polynomials.
You will need: graphing calculator

2. Lesson 1: Long Division
Use long division when the divisor is NOT a binomial.
Divide.

3. Lesson 2: Synthetic Division and the Remainder Theorem

4. Lesson 2: Synthetic Division and the Remainder Theorem
Synthetic: to combine or compose
Synthetic Division: Use ONLY when the divisor is a single degree binomial with a = 1; use to find factors/zeros of polynomials.
Divide.

5. Lesson 2: Synthetic Division and the Remainder Theorem
Divide.
Use the opposite number as the divisor -3
Write in the coefficients.
-3 |
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Bring down the 1st coefficient. Multiply, then add.

6. Lesson 2: Synthetic Division and the Remainder Theorem
= =
x³ – 3x² – x
x + 3
Remainder = 1 = f(-3) ÷

7. Lesson 3: Synthetic Division and the Factor Theorem
What this means: For factor (x – k), k is a zero of the polynomial when there is no remainder or f(k) = 0.

8. Lesson 3: Synthetic Division and the Factor Thm
Verify that (x + 2) and (x – 4) are factors of f, find the remaining factors, use the results to write the complete factorization, and list all real zeros of f, and then confirm using a graphing utility. |
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9. 2.3: DIGI Yes or No . 1. 2.