1. Multiplying and Dividing Polynomials
Algebra II with Trigonometry
Ms. Lee

2. Essential Question Essential Vocabulary
How do you multiply and divide polynomials?
How do you know if a polynomial will have a remainder?
Essential Vocabulary
Like Terms
Synthetic Division
Remainder Theorem

3. Multiplying Polynomials
Multiply each term of one polynomial by each term in the other polynomial.
Remember when multiplying variables with exponents, add the exponents.
Example: 𝑥 4 ∙ 𝑥 3 = 𝑥 7
MULTIPLICATION
Examples

4. Dividing Polynomials DIVISION
Long division of polynomials is like long division of numbers.
If a binomial goes into polynomial evenly (remainder of 0), then the binomial is a factor of the polynomial.
DIVISION

5. Synthetic Division
Synthetic division is a simplified method for dividing polynomials and uses only the coefficients of the polynomial.
We can use synthetic division to find all zeros/factors of a polynomial.
Examples

6. Remainder Theorem
If a polynomial P(x) of degree n is divided by (x – a), then the remainder is P(a).
In other words, when you plug a value into the polynomial, the solution is the remainder of the polynomial.
How is this theorem helpful for us?
Examples

7. Homework
Homework 6.2