Section 3-3 Dividing Polynomials

Objectives:Use Long Division and Synthetic Division to divide polynomials

Warm-Up ExamplesDivide Using Long Division

◦161 ÷ 7

◦12.18 ÷ 2.1

Divide ◦ 6x – 15y

3

Dividing PolynomialsPolynomial long division is a

method for dividing a polynomial by another polynomials of a lower degree. It is very similar to dividing numbers

Example: Divide Using Long Division

(–y2 + 2y3 + 25) ÷ (y – 3)

(15x2 + 8x – 12) ÷ (3x + 1)

Synthetic DivisionSynthetic 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)

Dividing Polynomials

Examples: Divide Using Synthetic Division

(3x4 – x3 + 5x – 1) ÷ (x + 2)

Examples: Divide Using Synthetic Division

(x2 – 3x – 18) ÷ (x – 6)

(6x2 – 5x – 6) ÷ (x + 3)

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

Example: Use Synthetic Substitution to evaluate the polynomial for the given value

P(x) = 2x3 + 5x2 – x + 7 for x = 2.

P(x) = x3 + 3x2 + 4 for x = –3.

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 x3 – x2 – 6x

HomeworkPages 170-172 #13-59