Chapter 5.1/5.2

Monomials and Polynomials

Vocabulary:• A monomial is an expression that is a number, a

variable, or the product of a number and one or more variables

They cannot contain variables in denominators,variables with exponents that are negative, or variables under radicals

• Constants are monomials that contain no variables

• The numerical factor of a monomial is the coefficient of the variable

Vocabulary:• The degree of a monomial is the sum of the

exponents of it variables – the degree of a constant is zero

• A power is an expression of the form X5

• Negative exponents are a way of expressing the multiplicative inverse of a number

Simplifying Expressions:• To simplify means to rewrite the expression

without parentheses or negative exponents

• Product of Powers: N3 x N5 = N8

• Quotient of Powers:

• Power of a Power: (N2)3 = N6

• Power of a Product: (NM)3 = N3 M3

42

6

NNN

More Vocab:• A Polynomial is a monomial or a sum of

monomials• The monomials that make up a polynomial are

called the terms of the polynomial• Like terms are the ones that can be combined

• Binomials (two terms) Trinomial (three terms)

• The degree is the degree of the monomial with the greatest degree

FOIL (multiply two binomials)• Find (3y + 2) (5y + 4)

• {(3y)(5y) + (3y)(4) + (2)(5y) + (2)(4)}

• = 15y2 + 12y + 10y + 8

• = 15y2 + 22y + 8

First terms Outer terms Inner terms Last terms

Tonight’s Homework:

Page 226 (19-41 odd)Page 231 (17-33 odd)Page 232 (37-49 odd)