Adding and subtracting polynomials 1L interpret expressions that represent a quantity in terms of its context

Vocabulary  The terms are the parts of and 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 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, x 2  A polynomial is a monomial or sum of monomials, each called a term of the polynomial. * A binomial is a polynomial with two terms. * A trinomial is a polynomial with three terms.

Vocabulary  The degree of a polynomial is the highest exponent.  1,2 and 3  Standard form is when a polynomial is written so that the exponents decrease from left to right.  The coefficient of the first term in Standard Form 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. a) 5x³ x b) x – 4x³ + x² c) -5 + x 8 – x 5

Adding Polynomials  When adding polynomials, like terms are combined. ***Exponents do not change when adding***  EX 3: (3x 4 – 2x 3 + 5x²) + (7x² + 9x 3 – 2x)

Practice 1. (8x² - 2x + 7) + (9x² + 6x – 11) 2. (4x – 3 – 5x³) + (3x² - 8x + 2)

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 x² + 3x³) – (8x³ - 3x² + 5)

Challenge! 1. (4x 2 + 7x 3 y 2 ) − (−6x 2 − 7x 3 y 2 − 4x) − (10x + 9x 2 ) 2. (−9xy 3 − 9x 4 y 3 ) + (3xy 3 + 7y 4 − 8x 4 y 4 ) + (3x 4 y 3 + 2xy 3 )