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Class Greeting

Lesson 6-1a Monomials and Factoring Chapter 6 - Factoring Lesson 6-1a Monomials and Factoring

Objective: The student will define the terms monomial, binomial, polynomial, factoring, factor, common factor, greatest common factor, integers, prime numbers, composite numbers and prime factorization. The students will discover and practice finding the greatest common factor.

Vocabulary a whole number whose factors are only 1 and itself 2, 3, 5, 7, 11, ... a whole number with more factors than just 1 and itself 4, 6, 8, 9, 10, …

Find the whole number factors of 22 Find the whole number factors of 22. Then classify it as prime or composite. 1 22 , 2 ,11, Answer: composite number Example 1-1a

Find the whole number factors of 31 Find the whole number factors of 31. Then classify it as prime or composite. 1 , 31 Answer: prime number. Example 1-1a

Find the whole number factors of each number Find the whole number factors of each number. Then classify each as prime or composite. a. 17 b. 25 Answer: 1, 17; prime Answer: 1, 5, 25; composite Example 1-1b

Vocabulary a number shown as a product of it’s primes 90 = 2 × 3 × 3 × 5

84 21 4 3 7 2 2 Find the prime factorization of 84. Use a factor tree. 21 4 3 7 2 2 All of the factors in the last branch of the factor tree are prime. Answer: or Example 1-2a

Find the prime factorization of 60. Answer: or Example 1-2b

To find the prime factorization of a negative integer, first factor out -1, then continue as you would with a positive integer.

Find the prime factorization of –132. / \ / \ / \ Answer: or Example 1-3a

Find the prime factorization of –154. Answer: Example 1-3b

Vocabulary 9.1 a monomial is in factored p475 form when it is shown as a product of prime numbers and no variable has exponent higher than 1.

Factor completely. Answer: Example 1-4a

Factor completely. 2 13 Answer: Example 1-4a

Factor each monomial completely. a. b. Answer: Answer: Example 1-4b

Vocabulary The greatest common factors of two or more numbers is the product of all the common prime factors. The GCF of 48 and 60 is 12, (2 × 2 × 3).

Find the GCF of 12 and 18. or 6. Answer: the GCF is Example 1-5a

Find the GCF of Answer: 3ab Example 1-5a

3x(x – 5) = 3 x (x – 5) Find the GCF of 4(x – 5), 3x(x – 5).

Find the GCF of each set of monomials. a. 15 and 35 b. c. 5(x + 2) and 13(x + 2) and Answer: 5 Answer: Answer: ( x + 2) Example 1-5b

Lesson Summary: Objective: The student will define the terms monomial, binomial, polynomial, factoring, factor, common factor, greatest common factor, integers, prime numbers, composite numbers and prime factorization. The students will discover and practice finding the greatest common factor.

Preview of the next Lesson: Objective: The student will discover and demonstrate how to factor polynomials with common factors.

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