Chapter 4
4-1: Factors and Monomials
OBJECTIVES:

Determine whether one number is a factor of another.

Determine whether an expression is a monomial.
VOCABULARY:
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Factors: Two or more numbers that are multiplied to form a product.
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Divisible: When you divide and you get a remainder of 0.
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Monomial: A number, a variable, or a PRODUCT of numbers and/or variables.
Notes:
Divisibility Rules:
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A number is divisible by 2 if the ones digit is divisible by 2.
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A number is divisible by 3 if the sum of its digits is divisible by 3.
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A number is divisible by 5 if the ones digit is 0 or 5.
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A number is divisible by 6 if the number is divisible by 2 and 3.
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A number is divisible by 10 if the ones digit is 0.
Note on identifying Monomials:
A monomial is a product of variables and rational numbers and may have a number as a denominator, but not a variable.
4-2: Powers and Exponents
Objectives:

Write expressions using exponents.

Evaluate expressions containing exponents.
VOCABULARY:

Base: The number that is multiplied.
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Exponent: How many times the base is used as a factor.
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Power: The number that can be expressed using an exponent.
Notes:

Very important to know how to “say” powers.
Remember: Any number raised to the zero power is equal to 1
4-3: Prime Factorization
Objectives:

Write the prime factorizations of composite numbers.

Factor Monomials.
VOCABULARY:
Prime Number: A whole number that has exactly two factors, one and itself.
Composite Number : A whole number that has more than two factors.
Prime Factorization: When a composite number is expressed as the product of prime factors.
Factor Tree: A method for finding a prime factorization of a number.
Factor: To write a number as a product of its factors.
Notes:


When “factoring” monomials, if the monomial is negative, you must include -1 as one of the factors.
When “factoring” a non-negative monomial, you should not include a 1 as a factor.
4-4: Greatest Common Factor (GCF)
Objectives:

Find the greatest common factor of two or more numbers or monomials.

Use the distributive property to factor algebraic expressions.
VOCABULARY:
Greatest Common Factor: The greatest number that is a factor of two or more numbers.
Notes:
Factor Algebraic Expressions: You can find the GCF of two or more monomials by finding the product of their
common prime factors.
4-5: Simplifying Algebraic Fractions
Objectives:

Simplify fractions using the GCF.

Simplify algebraic fractions.
VOCABULARY
Simplest Form: When the GCF of the numerator and denominator is 1.
Algebraic Fraction: A fraction with variables in the numerator or denominator.
Remember: When simplifying fractions, if a common factor is used that is NOT the GCF, the resulting fraction will not be in simplest form, which
means you will have to simplify again.
4-6: Multiplying and Dividing Monomials
Objectives:

Multiply Monomials.

Divide Monomials.
Notes:
1.
2.
Product of Powers: When you multiply powers with the same base, you add their exponents.
Quotient of Powers: When you divide powers with the same base, you subtract their exponents.
4-7: Negative Exponents
Objectives:


Write expressions using negative exponents.
Evaluate numerical expressions containing negative exponents.
Notes:


Negative exponents must be rewritten with a positive exponent using the following rule:
Algebraic expressions containing negative exponents can be written using positive exponents and evaluated.
4-8: Scientific Notation
Objectives:


Express numbers in standard form and in scientific notation.
Compare and order numbers written in scientific notation.
VOCABULARY
Scientific Notation: method for writing very large numbers or very small numbers.
Notes:

A number is expressed in scientific notation when it is written as the product of a factor and a power of 10. The factor must be
greater than or equal to 1 and less than 10.
Positive and Negative Exponents in Scientific Notation:


When the number is 1 or greater, the exponent is positive.
When the number is between 0 and 1, the exponent is negative.