Adding and Subtracting Polynomials 8-1 Notes Algebra 1 Adding and Subtracting Polynomials

8.1 pg. 468 20-51, 66-90(x3)

6th degree, 7th degree, etc… Polynomial A monomial or the sum of monomials. (Each called a term) Some have special names (Monomial, Binomial and Trinomials) The degrees of the polynomials are: Degree Name Constant 1 Linear 2 Quadratic 3 Cubic 4 Quartic 5 Quintic 6 or more 6th degree, 7th degree, etc…

Example 1: Identify polynomials Determine whether each expression is a polynomial. If it is a polynomial, find the degree and determine whether it is a monomial, binomial, or trinomial. 1.) 6𝑥−4 2.) 𝑥 2 +2𝑥𝑦−7 3.) 14𝑑+19𝑒 3 5𝑑 4 4.) 26𝑏 2

Example 1: Identify polynomials Determine whether each expression is a polynomial. If it is a polynomial, find the degree and determine whether it is a monomial, binomial, or trinomial. 1.) 6𝑥−4 (Yes, Linear, Binomial) 2.) 𝑥 2 +2𝑥𝑦−7 (Yes, Quadratic, Trinomial) 3.) 14𝑑+19𝑒 3 5𝑑 4 (Not a polynomial) 4.) 26𝑏 2 (Yes, Quadratic, Monomial)

Standard form of a polynomial Terms are listed in order from highest degree to lowest. When written in this form, the coefficient of the first term is called the leading coefficient.

Example 2: Standard of a Polynomial Write each polynomial in standard form. Identify the leading coefficient. 1.) 9𝑥 2 + 3𝑥 6 −4𝑥 2.) 12+5𝑦+6𝑥𝑦+8𝑥𝑦 2

Example 2: Standard of a Polynomial Write each polynomial in standard form. Identify the leading coefficient. 1.) 9𝑥 2 + 3𝑥 6 −4𝑥 2.) 12+5𝑦+6𝑥𝑦+8𝑥𝑦 2 3𝑥 6 + 9𝑥 2 −4𝑥; 3 8𝑥𝑦 2 +6𝑥𝑦+5𝑦+12; 8

Example 3: Add Polynomials Find each Sum 1.) 7𝑦 2 +2𝑦−3 + 2−4𝑦+5𝑦 2 2.) 4𝑥 2 −2𝑥+7 + 3𝑥−7𝑥 2 −9

Example 3: Add Polynomials Find each Sum 1.) 7𝑦 2 +2𝑦−3 + 2−4𝑦+5𝑦 2 12𝑦 2 −2𝑦−1 2.) 4𝑥 2 −2𝑥+7 + 3𝑥−7𝑥 2 −9 −3𝑥 2 +𝑥−2

Example 4: Subtracting Polynomials Find each Difference 1.) 6𝑦 2 + 8𝑦 4 −5𝑦 − 9𝑦 4 −7𝑦+2𝑦 2 2.) 6𝑛 2 +11 𝑛 3 +2𝑛 − 4𝑛−3+5𝑛 2

Example 4: Subtracting Polynomials Find each Difference 1.) 6𝑦 2 + 8𝑦 4 −5𝑦 − 9𝑦 4 −7𝑦+2𝑦 2 −𝑦 4 + 4𝑦 2 +2𝑦 2.) 6𝑛 2 +11 𝑛 3 +2𝑛 − 4𝑛−3+5𝑛 2 11𝑛 3 + 𝑛 2 −2𝑛+3

Example 5: Add and Subtract Polynomials VIDEO GAMES The total amount of toy sales 𝑇 (in billions of dollars) consists of two groups: sales of video games V and sales of tradition toys 𝑅. In recent years, the sales of traditional toys and total sales could be represented by the following equations, where 𝑛 is the number of years since 2000. 𝑅= 0.46𝑛 3 − 1.9𝑛 2 +3𝑛+19 𝑇= 0.45𝑛 3 − 1.85𝑛 2 +4.4𝑛+22.6 1.) Write an equation that represents the sales of video games 𝑉. 2.) Use the equation to predict the amount of video game sales in the year 2012.

Example 5: Add and Subtract Polynomials VIDEO GAMES The total amount of toy sales 𝑇 (in billions of dollars) consists of two groups: sales of video games V and sales of tradition toys 𝑅. In recent years, the sales of traditional toys and total sales could be represented by the following equations, where 𝑛 is the number of years since 2000. 𝑅= 0.46𝑛 3 − 1.9𝑛 2 +3𝑛+19 𝑇= 0.45𝑛 3 − 1.85𝑛 2 +4.4𝑛+22.6 1.) Write an equation that represents the sales of video games 𝑉. 𝑉=−0.01 𝑛 3 + 0.05𝑛 2 +1.4𝑛+3.6 2.) Use the equation to predict the amount of video game sales in the year 2012. 10.32 𝑏𝑖𝑙𝑙𝑖𝑜𝑛 𝑑𝑜𝑙𝑙𝑎𝑟𝑠