Adding and subtracting polynomials TUESDAY AUGUST 13TH MATH I Book – p. 59

Vocabulary The terms are the parts of an expression that are added together. The coefficient of the term is the number part of a term with a variable. A constant term has a number part but no variable part. Like terms are terms that have the same variable parts. Ex: -x2 and 2x2 are like terms. (constant terms are also like terms) EX 1: Identify the terms, coefficients, constants: -x + 2x + 8

Vocabulary A monomial is a number, a variable, or the product of a number and one or more variables with whole number exponents. Ex: 8x, 3, x2 A polynomial is a monomial or sum of monomials, each called a term of the polynomial. Ex. 8x + 2 – 5x2 A binomial is a polynomial with two terms. Ex: 2x + 3 A trinomial is a polynomial with three terms. Ex: 6x4 + 5 – 3x

Vocabulary The degree of a polynomial is the highest exponent. If the degree of the polynomial is 1, it is linear. If the degree of the polynomial is 2, it is quadratic. If the degree of the polynomial is 3, it is cubic. Standard form is when a polynomial is written so that the exponents decrease from left to right. The coefficient of the first term is called the leading coefficient. EX 2: Put the following polynomials in order so the exponents decrease from left to right and name the leading coefficient and degree of the polynomial. 5x³ - 4 + 3x x – 4x³ + x² -5 + x8 – x5

Adding Polynomials When adding polynomials, like terms are combined. ***Exponents do not change when adding*** EX 3: (3x4 – 2x3 + 5x²) + (7x² + 9x3 – 2x)

Practice 1. (8x² - 2x + 7) + (9x² + 6x – 11)

Subtracting polynomials When subtracting polynomials, distribute the negative to all terms in the second polynomial and then combine like terms. EX 4: (2x³ - 5x² - 5) – (4x³ - 5x² + x – 4)

Practice 3. (3x² - 8x + 3) – (9x + 2x² - 8) 4. (5x + 2 - x² + 3x³) – (8x³ - 3x² + 5)

Classwork Adding and Subtracting Polynomials Worksheet ** DUE AT THE END OF CLASS! **