Chapter 4 Working with Polynomials Important Terms

Constant A number – Examples: 4, -1, 2/3, 0

Monomial Mono means one A constant, a variable, or a product of a constant and a variable(s) – Examples: -9, x, -6xy, 17x²y

Coefficient Also known as numerical coefficient Constant factor in a monomial Number being multiplied to a variable – Example: 8x 8 is the coefficient

Degree of a variable The number of times the variable occurs as a factor Look at the power of the variable Example: 6x² The degree of x is 2

Degree of a monomial The sum of the degrees of the variables in the monomial The constant has zero degree – Example: 3xy² has a degree of 3 – Example: 9 has a degree of 0 – Example: w has a degree of 1

Polynomial A monomial or a sum of monomials The monomials are known as the terms – Example: 9x² - 10x + 8 The terms are 9x², -10x, and 8

Degree of a polynomial The greatest degree of its terms after it has been simplified. – Example: The polynomial has degree 5

Adding & Subtracting Polynomials Combine like terms – Terms must have the same exact variables and degrees – Add/subtract the coefficients of the terms – Answers must be written in ascending or descending order (according to the degree of the variable)

Examples Arrange the terms in order of decreasing degree of x. – 1. – 2.

Examples 1.Add and

Examples Subtract from

Examples Simplify

Examples Simplify