Download Prime Factorization

Prime Factorization
Section 9.2
Objectives:
Write the prime factorizations of composite numbers
Factor monomials
Notes: Write Prime Factorizations
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Numbers that have whole number factors can be represented using rectangles- Example:
A _______________________ is a whole number that has exactly two unique factors, 1 and
itself. So 5 is a prime number.
A _______________________ is a whole number that has more than two factos. The
numbers 6 and 8 are composite numbers.
* The numbers 0 and 1 are neither prime nor composite.
Notes: Write Prime Factorizations
Prime Number
Factors
Composite Number
Factors
2
1,2
4
1,2,4
3
1,3
6
1,2,3,6
5
1,5
8
1,2,4,8
Examples
• Determine whether each number is prime or composite:
• 1. 15
• 2. 37
Notes
• When a composite number is expressed as the product of prime factors, it is
called the __________________ of the number.
• One way to find the prime factorization of a number is to use a
______________.
• Step 1: Write the number that you are factoring at the top.
• Step 2: Choose any pair of whole number factors of the number.
• Step 3: Continue to factor any number that is not prime.
• The factor tree is complete when you have a row of prime numbers. The
prime factorization of 20 is ________________________.
Examples
• What is the prime factorization?
• 3. 24
• 4. 90
Notes: Factor Monomials
• A ______________ is a number, a variable, or a product of numbers and/or
variables.
Monomials
Not Monomials
80, x, 8x
x + 5, 𝑥 2 -𝑦 2
• Recall that to factor a number means to write it as a product of its factors.
• A monomial can also be factored as a product of prime numbers and variables
with no exponent greater than 1.
• Negative coefficients can be factored using -1 as a factor.
Study Tip: Factors
• In the equation 8 x 10 = 80, 8 and 10 are factors of 80.
• In the equation 8
x = 8x, 8 and x are factors of 8x.
Examples
• Factor each monomial:
• 1. 11𝑟 4s
• 2.-28𝑎2𝑏3
Practice
• Factor each monomial:
• 1. 15y
• 2. 20qrs
• 3. -𝑝4
Practice
• 4. The surface area of a cube is given by the expression 6𝑠2 , where s is the
side length. Factor 6𝑠 2 .
• 5. Write three different monomials that have factors of 2, 5, and 𝑎2
Writing in Math
• Suppose n represents a prime number. Is 2n always, sometimes, or never
prime? Explain your reasoning.
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