1. Class Greeting

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

3. 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.

4. 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, …

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

6. 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

7. 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

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

9. 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

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

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

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

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

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

15. Factor completely.
Answer:
Example 1-4a

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

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

18. 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).

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

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

21. 3x(x – 5) = 3 x (x – 5) Find the GCF of 4(x – 5), 3x(x – 5).

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

23. 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.

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

25. Kahoot!

26. Stand Up Please