Lesson 9.1 Add and Subtract Polynomials Essential Question: How do you add and subtract polynomials?

Before we start… # of Males: 𝑥 2 +4𝑥+2 # of Females: 2 𝑥 2 +3𝑥+1 What is the total number of students in the school?

What is a monomial? A number, a variable, or the product of a number and one or more variables Whole number exponents 4𝑥𝑦

Expression Monomial? 5+𝑥 4𝑎𝑏𝑐 𝑥 −1 2 𝑛 6 𝑥 2 7 𝑥 𝑥

What is a degree of a monomial? The sum of the exponents of the variables 𝟐+𝟏=𝟑 3 𝑥 2 𝑦

Monomial Degree 10 3𝑥 1 2 𝑎 𝑏 2 −1.8 𝑚 5

What is a polynomial? 3 𝑥 2 −5𝑥+8 A monomial or a sum of monomials Each monomial is a term Written in descending order 3 𝑥 2 −5𝑥+8

What is the degree of a polynomial? The greatest degree or exponent of its terms Degree 2 𝑥 3 + 𝑥 2 −5𝑥+12

What is a leading coefficient? The coefficient of the first term when written in descending order 2 𝑥 3 + 𝑥 2 −5𝑥+12 Leading coefficient

Rewrite the polynomial and identify the degree and leading coefficient. 15𝑥− 𝑥 3 +3 5𝑦−2 𝑦 2 +9

How do you classify a polynomial? By degree and the number of terms. Degree Name Constant 1 Linear 2 Quadratic 3 Cubic 4 Quartic 5th and Up Nth Degree # of terms Name 1 monomial 2 binomial 3 trinomial

If it’s a polynomial, classify it. Expression Is it a polynomial? Classification 9 2 𝑥 2 +𝑥−5 6 𝑛 4 − 8 𝑛 𝑛 −2 −3 7𝑏 𝑐 3 +4 𝑏 4 𝑐 𝑥 3 −4 𝑥 2 +𝑥−5

How do you add and subtract polynomials? To add, add like terms. To subtract, add its opposite. Remember like terms must also have the same exponent.

3 𝑥 2 +𝑥−6 + 𝑥 2 +4𝑥+10

4 𝑛 2 +5 − −2 𝑛 2 +2𝑛−4

Baseball Attendance Major League Baseball teams are divided into two leagues. During the period 1995-2001, the attendance N and A (in thousands) at National and American League baseball games, respectively, can be modeled by 𝑁=−488 𝑡 2 +5430𝑡+24,700 𝐴=−318 𝑡 2 +3040𝑡+25,600 where t is the number of years since 1995. About how many people attended Major League Baseball games in 2001?

How do you add and subtract polynomials?

Ticket Out the Door 4 𝑥 3 +2 𝑥 2 −4 + 𝑥 3 −3 𝑥 2 +𝑥