Monomials

1
Monomials

• An expression that is either
• a number,
• a variable,
• or a product of numerals and variables with whole
  number exponents.

2
Monomials

• 5x3y12 is a monomial
• is not a monomial
• is not a monomial

3
Vocabulary

• Constants
• monomials that contain no variables
• Example 3 or -22
• Coefficient
• Numeric factor of the term
• -32x3y12z15 coefficient -32

4
Vocabulary (continued)

• Degree of a Monomial
• The sum of the exponents of the variables
• 3x4 degree 4
• -32x3y12z15 degree 31215
• 30
• 5 degree 0

5
Vocabulary (continued)

• Power
• An expression in the form of xn
• Can also refer to the exponent

6
Product of Powers

• For any real number a and integers m and n,
• am an amn
• 23 25
• 2 2 2 2 2 2 2 2 28

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Quotient of Powers

• For any real number a and integers m and n,

8
Quotient of Powers

• Find the quotient

9
NEGATIVE EXPONENTS

• For any real number a?0 and any integer n, a-n

10
Vocabulary (continued)

• Simplify
• rewrite expression
• No parenthesis
• No negative exponents
• Multiply variables
• Combine like terms

11
Simplify

• (-2a3b)(-5ab4)
• Multiply Coefficients
• (-2)(-5)10
• Multiply Variables
• (a3)(a) a4
• (b)(b4) b5
• 10a4b5

12
Simplify

• Try this one

13
PROPERTIES OF POWERS

• Power of a Power (am)namn
• Power of a Product (ab)mambm
• Power of a Quotient

14
Properties of Powers
15
Scientific Notation

• FORM a x 10n
• n is an integer
• Write in Scientific Notation
• 4,560,000
• 0.000092

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Multiply Numbers inScientific Notation

• (a x 10n) (b x 10m) (ab x 10nm)
• Check and make sure
• (1.8 x 104) (4 x 107)
• (5 x 103) (7 x 108)

17
Divide Numbers inScientific Notation

• Check and make sure

18
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

19
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

20
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
21
Simplify

• (2a35a-7) (a3-3a2)
• 3a32a-5
• (3b32b2-4b3) - (b3-2b23b-4)
• 2b34b2-7b7
• -3y(4y22y-3)
• -12y3 - 6y2 9y

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Polynomial Vocabulary(continued)

• Leading Term
• The term with the highest degree
• Leading Coefficient
• The coefficient of the leading term

23
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

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Multiplying Polynomials
25
Multiplying Polynomials