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Monomials. An expression that is either a number, a variable, or a product of numerals and variables with whole number exponents. Monomials. 5x 3 y 12 is a monomial is not a monomial is not a monomial. Vocabulary. Constants monomials that contain no variables

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monomials
Monomials

An expression that is either

a number,

a variable,

or a product of numerals and variables with whole number exponents.

monomials1
Monomials

5x3y12 is a monomial

is not a monomial

is not a monomial

vocabulary
Vocabulary
  • Constants

monomials that contain no variables

Example 3 or -22

  • Coefficient

Numeric factor of the term

-32x3y12z15 coefficient = -32

vocabulary continued
Vocabulary (continued)
  • Degree of a Monomial

The sum of the exponents of the variables

3x4 degree = 4

-32x3y12z15 degree = 3+12+15

= 30

5 degree = 0

vocabulary continued1
Vocabulary (continued)
  • Power

An expression in the form of xn

Can also refer to the exponent

product of powers
Product of Powers
  • For any real number a and integers m and n,

am · an =am+n

23 · 25

=2 · 2 · 2 · 2 · 2 · 2 · 2 · 2= 28

quotient of powers
Quotient of Powers
  • For any real number a and integers m and n,
quotient of powers1
Quotient of Powers
  • Find the quotient
negative exponents
NEGATIVE EXPONENTS
  • For any real number a≠0 and any integer n, a-n=
vocabulary continued2
Vocabulary (continued)

Simplify

rewrite expression

  • No parenthesis
  • No negative exponents
  • Multiply variables
  • Combine like terms
simplify
Simplify

(-2a3b)(-5ab4)

  • Multiply Coefficients

(-2)(-5)=10

  • Multiply Variables

(a3)(a) = a4

(b)(b4) = b5

  • 10a4b5
simplify1
Simplify
  • Try this one
properties of powers
PROPERTIES OF POWERS
  • Power of a Power: (am)n=amn
  • Power of a Product: (ab)m=ambm
  • Power of a Quotient:
polynomials
Polynomials

A monomial or a sum of monomials.

Monomial – a polynomial with exactly one term

Binomial – a polynomial with exactly two terms

Trinomial – a polynomial with exactly three terms

polynomial vocabulary
Polynomial Vocabulary
  • Term

Each monomial in a polynomial

  • Like Terms

Terms whose variable factors are exactly the same

  • Degree of the Polynomial

The highest degree of its terms

polynomials1
Polynomials
  • Indicate if the following is a polynomial,
  • If so classify according to the number of terms
  • Indicate the degree of the polynomial

Not a polynomial

Polynomial- Binomial- 9

polynomial vocabulary continued
Polynomial Vocabulary(continued)
  • Leading Term

The term with the highest degree

  • Leading Coefficient

The coefficient of the leading term

descending order
Descending Order
  • A polynomial is written in descending order for the variable x when the term with the greatest exponent for x is first, and each subsequent term has an exponent for x less than the prior term.
  • Example: Write the following in descending order for the variable a.

4a4 + a2 - 7a3 +6a5 + 12a8 + 4

12a8 + 6a5 + 4a4 - 7a3 + a2 + 4

2a 3 5a 7 a 3 3a 2 3a 3 2a 5 3b 3 2b 2 4b 3 b 3 2b 2 3b 4 2b 3 4b 2 7b 7 3y 4y 2 2y 3 12y 3 6y 2 9y
(2a3+5a-7) + (a3-3a+2)

3a3+2a-5

(3b3+2b2-4b+3) - (b3-2b2+3b-4)

2b3+4b2-7b+7

-3y(4y2+2y-3)

-12y3 - 6y2 + 9y

Simplify