Section 8.1 Day 1 Adding and Subtracting Polynomials Algebra 1

Learning Targets Define polynomial, trinomial, binomial, and leading coefficient Classify a polynomial by its degree and corresponding name Write a polynomial in standard form Add polynomials Subtract polynomials

Topic 1: Classifying Polynomials by Terms Algebra 1 Section 8.1 Day 1

Definitions Monomial: an algebraic expression with one term Polynomial: an algebraic expression that meets the conditions below No division by a variable Exponents must be ≥0 Finite number of terms Binomial: an algebraic expression with two terms 7 minutes Trinomial: an algebraic expression with three terms

Polynomial 3 𝑥 4 −2 𝑥 2 +4𝑥−7 Monomial 8 𝑥 5 Trinomial 6 𝑥 8 +9𝑥−5 Binomial 4𝑥+12 Not Polynomials 9 𝑥 −4 +2𝑥 4 𝑥+2 −10 𝑥 2 −3

Classifications and Examples Degree Degree Classification Type of Polynomial 6  Monomial (1)  𝟑𝒙−𝟓 Binomial (2) 𝟏 𝟐 𝒙 𝟐 −𝟑𝒙+𝟐 Trinomial (3)   𝒙 𝟑 −𝟐𝒙   𝒙 𝟒 +𝟑 𝒙 𝟑 −𝟐 𝒙 𝟐 −𝟕𝒙+𝟏 Polynomial (5)   𝒙 𝟓 −𝟓 𝒙 𝟒 +𝟓 𝒙 𝟑 +𝟓 𝒙 𝟐 −𝟔𝒙+𝟏 Polynomial (6) Example Degree Degree Classification Type of Polynomial 6   𝟑𝒙−𝟓 𝟏 𝟐 𝒙 𝟐 −𝟑𝒙+𝟐   𝒙 𝟑 −𝟐𝒙   𝒙 𝟒 +𝟑 𝒙 𝟑 −𝟐 𝒙 𝟐 −𝟕𝒙+𝟏   𝒙 𝟓 −𝟓 𝒙 𝟒 +𝟓 𝒙 𝟑 +𝟓 𝒙 𝟐 −𝟔𝒙+𝟏

Topic 2: Standard Form of a Polynomial Algebra 1 Section 8.1 Day 1

Standard Form of a Polynomial Key Terms Standard Form of a Polynomial Terms are listed from the highest degree to the lowest degree. Not in Standard Form 3−5 𝑥 2 +8 𝑥 5 − 𝑥 3 In Standard Form 8 𝑥 5 − 𝑥 3 −5 𝑥 2 +3 Leading Coefficient The coefficient in front of the highest degree term. Ex: In the previous example, the leading coefficient would be 8

Practice Set 1 1. 3 𝑥 2 +4 𝑥 5 −7𝑥 2. 5𝑦−9−2 𝑦 4 −6 𝑦 3 Directions: Rewrite the polynomials into standard form. Then, identify the leading coefficient. 1. 3 𝑥 2 +4 𝑥 5 −7𝑥 Standard Form: 4 𝑥 5 +3 𝑥 2 −7𝑥 Leading Coefficient: 4 2. 5𝑦−9−2 𝑦 4 −6 𝑦 3 Standard Form: −2 𝑦 4 −6 𝑦 3 +5𝑦−9 Leading Coefficient: −2

Topic 3: Classifying Polynomials by Degree Algebra 1 Section 8.1 Day 1

Definitions Degree of a Polynomial is the largest exponent in the polynomial. Example: The degree of 5 𝑥 13 +6 𝑥 4 −1 is 13.

Classifications and Examples Degree Degree Classification Type of Polynomial 6   𝟑𝒙−𝟓 1 𝟏 𝟐 𝒙 𝟐 −𝟑𝒙+𝟐 2   𝒙 𝟑 −𝟐𝒙 3   𝒙 𝟒 +𝟑 𝒙 𝟑 −𝟐 𝒙 𝟐 −𝟕𝒙+𝟏 4   𝒙 𝟓 −𝟓 𝒙 𝟒 +𝟓 𝒙 𝟑 +𝟓 𝒙 𝟐 −𝟔𝒙+𝟏 5 Example Degree Degree Classification Type of Polynomial 6   𝟑𝒙−𝟓 𝟏 𝟐 𝒙 𝟐 −𝟑𝒙+𝟐   𝒙 𝟑 −𝟐𝒙   𝒙 𝟒 +𝟑 𝒙 𝟑 −𝟐 𝒙 𝟐 −𝟕𝒙+𝟏   𝒙 𝟓 −𝟓 𝒙 𝟒 +𝟓 𝒙 𝟑 +𝟓 𝒙 𝟐 −𝟔𝒙+𝟏

Classifications and Examples Degree Degree Classification Type of Polynomial 6  Constant  𝟑𝒙−𝟓 1 Linear 𝟏 𝟐 𝒙 𝟐 −𝟑𝒙+𝟐 2 Quadratic   𝒙 𝟑 −𝟐𝒙 3 Cubic   𝒙 𝟒 +𝟑 𝒙 𝟑 −𝟐 𝒙 𝟐 −𝟕𝒙+𝟏 4 Quartic   𝒙 𝟓 −𝟓 𝒙 𝟒 +𝟓 𝒙 𝟑 +𝟓 𝒙 𝟐 −𝟔𝒙+𝟏 5 Quintic

Classifications and Examples Degree Degree Classification Type of Polynomial 6  Constant Monomial (1)  𝟑𝒙−𝟓 1 Linear Binomial (2) 𝟏 𝟐 𝒙 𝟐 −𝟑𝒙+𝟐 2 Quadratic Trinomial (3)   𝒙 𝟑 −𝟐𝒙 3 Cubic   𝒙 𝟒 +𝟑 𝒙 𝟑 −𝟐 𝒙 𝟐 −𝟕𝒙+𝟏 4 Quartic Polynomial (5)   𝒙 𝟓 −𝟓 𝒙 𝟒 +𝟓 𝒙 𝟑 +𝟓 𝒙 𝟐 −𝟔𝒙+𝟏 5 Quintic Polynomial (6)

Classifications and Graphs Example Degree Degree Classification Graphs 6  Constant Graph in Calc  𝟑𝒙−𝟓 1 Linear

Classifications and Graphs Example Degree Degree Classification Graphs 𝟏 𝟐 𝒙 𝟐 −𝟑𝒙+𝟐 2 Quadratic Graph in Calc   𝒙 𝟑 −𝟐𝒙 3 Cubic

Classifications and Graphs Example Degree Degree Classification Graphs   𝒙 𝟒 +𝟑 𝒙 𝟑 −𝟐 𝒙 𝟐 −𝟕𝒙+𝟏 4 Quartic Graph in Calc   𝒙 𝟓 −𝟓 𝒙 𝟒 +𝟓 𝒙 𝟑 +𝟓 𝒙 𝟐 −𝟔𝒙+𝟏 5 Quintic

Summary of a Polynomial’s Degree Degree of a Polynomial Largest Exponent Indicates the maximum number of real zeros/roots a function could consist of (could be less) Indicates the maximum number of real solutions a function could have (could be less) Example: 𝟒 𝒙 𝟑 −𝟐𝒙 Largest Exponent: 3 There are 3 real zeros/roots at MOST. There are 3 real solutions at MOST. **Note: Zeros, roots, and solutions essentially represent the same concept.

SMART Goal #1 Check in Tracking Sheet Example Group Leaders 1. On a piece of paper, please track the accomplishments of your group members progress to achieving their goals. 2. If they accomplish the goal the next day, please put a star to represent their success. Tracking Sheet Example Name 1/10 Homework 1/11 1/12 Person 1 None Work on Section 1.2 HW Person 2 Revise Notes Person 3 Make Flash Cards for 1.2 Day 1 Make Flash Cards for 1.2 Day 2 Person 4 Set up time to meet with teacher Meet with teacher for section 1.2