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