1. Prime Factorization Section 9.2 Objectives: Write the prime factorizations of composite numbers Factor monomials

2. Notes: Write Prime Factorizations 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.

3. Notes: Write Prime Factorizations Prime NumberFactors 21,2 31,3 51,5 Composite NumberFactors 41,2,4 61,2,3,6 81,2,4,8

4. Examples Determine whether each number is prime or composite: 1. 15 2. 37

5. 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 ________________________.

6. Examples What is the prime factorization? 3. 24 4. 90

7. Notes: Factor Monomials A ______________ is a number, a variable, or a product of numbers and/or variables. 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. MonomialsNot Monomials 80, x, 8x

8. 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.

9. Examples

10. Practice

12. Writing in Math Suppose n represents a prime number. Is 2n always, sometimes, or never prime? Explain your reasoning. _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________