1. Section 3-3 Dividing Polynomials Objectives: Use Long Division and Synthetic Division to divide polynomials

2. Warm-Up Examples Divide Using Long Division ◦ 161 ÷ 7 ◦ 12.18 ÷ 2.1 Divide ◦ 6x – 15y 3

3. Dividing Polynomials Polynomial long division is a method for dividing a polynomial by another polynomials of a lower degree. It is very similar to dividing numbers

4. Example: Divide Using Long Division (–y 2 + 2y 3 + 25) ÷ (y – 3) (15x 2 + 8x – 12) ÷ (3x + 1)

5. Synthetic Division Synthetic division is a shorthand method of dividing a polynomial by a linear binomial by using only the coefficients. For synthetic division to work, the polynomial must be written in standard form, using 0 and a coefficient for any missing terms, and the divisor must be in the form (x – a)

6. Dividing Polynomials

7. Examples: Divide Using Synthetic Division (3x 4 – x 3 + 5x – 1) ÷ (x + 2)

8. Examples: Divide Using Synthetic Division (x 2 – 3x – 18) ÷ (x – 6) (6x 2 – 5x – 6) ÷ (x + 3)

9. Synthetic Substitution You can use synthetic division to evaluate polynomials. This process is called synthetic substitution. The process of synthetic substitution is exactly the same as the process of synthetic division, but the final answer is interpreted differently, as described by the Remainder Theorem

10. Example: Use Synthetic Substitution to evaluate the polynomial for the given value P(x) = 2x 3 + 5x 2 – x + 7 for x = 2. P(x) = x 3 + 3x 2 + 4 for x = –3.

11. Geometry Application Write an expression that represents the area of the top face of a rectangular prism when the height is x + 2 and the volume of the prism is x 3 – x 2 – 6x

12. Homework Pages 170-172 #13-59