1. Lesson 5-1/5-2 Polynomials & Adding/Subtracting Objective Students will: Evaluate polynomial functions Simplify polynomials by collecting like terms Add/Subtract polynomials Find the additive inverse of polynomials

2. Polynomials A collection of terms: 2x3x – 4x 3 – 2x 2 y + 8 Coefficients: numbers in front of each term Degree of a term: sum of exponents acting on the variables Degree of polynomials: equal to highest degree of any term Names: monomial, binomial, trinomial

3. General form (descending order): a n x n + a n-1 x n-1 + …+ a 1 x + a 0 Polynomial Functions: Evaluate by plugging in P(x) = x 2 – 5x + 8 when x = 6 P(6) = 6 2 – 5(6) + 8 = 14 Simplifying Polynomials: combine like terms (same variable parts)

4. Example 1 Simplify, state the degree, and give the specific name. 2x 2 y – 4x + 4y – 3xy 2 + x 2x 2 y – 3xy 2 – 3x + 4y Degree: 3 (x 2 y 1 = 2+1) Name: More than 3 terms so just polynomial will do! Adding/Subtracting Polynomials Combine like terms: A) Mark like terms Or B) line up vertically Additive Inverse: Polynomial with all opposite terms EX: 2x 2 -3x + 5 Additive inverse: -2x 2 + 3x -5 When problem is subtraction, Change to add the inverse!!!

5. Example 2 Subtract (change to additive inverse) Method A) Mark LikeTerms (4xy 2 – 6x 2 y 2 + 5x 3 y 2 ) – (2xy 2 + 4x 2 y 2 – 8x 3 y 2 ) (4xy 2 – 6x 2 y 2 + 5x 3 y 2 ) + (-2xy 2 - 4x 2 y 2 + 8x 3 y 2 ) 2xy 2 - 10x 2 y 2 + 13x 3 y 2 )

6. Example 2 Subtract (change to additive inverse) Method B) Line up Vertically (4xy 2 – 6x 2 y 2 + 5x 3 y 2 ) – (2xy 2 + 4x 2 y 2 – 8x 3 y 2 ) (4xy 2 – 6x 2 y 2 + 5x 3 y 2 ) + (-2xy 2 - 4x 2 y 2 + 8x 3 y 2 ) 2xy 2 - 10x 2 y 2 + 13x 3 y 2

7. You Try (5xy 4 - 7xy 2 + 4x 2 - 3) – (-3xy 4 + 2xy 2 - 2y + 4)

8. Assignment 5-1/208 / 3- 31 eoo, 41-49o 5-2/ 212-213/1-29 eoo, 37, 45