Monomials

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# Monomials - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Monomials' - guang

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Presentation Transcript
Monomials

An expression that is either

a number,

a variable,

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

Monomials

5x3y12 is a monomial

is not a monomial

is not a monomial

Vocabulary
• Constants

monomials that contain no variables

Example 3 or -22

• Coefficient

Numeric factor of the term

-32x3y12z15 coefficient = -32

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 (continued)
• Power

An expression in the form of xn

Can also refer to the exponent

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

Simplify

rewrite expression

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

(-2a3b)(-5ab4)

• Multiply Coefficients

(-2)(-5)=10

• Multiply Variables

(a3)(a) = a4

(b)(b4) = b5

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

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)

The term with the highest degree

The coefficient of the leading term

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

(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