This document introduces factoring integers and monomials. It defines prime and composite numbers, and explains how to find the greatest common factor (GCF) of integers and the prime factorization of a number. It also shows how to find a missing factor given a monomial and one of its factors. Examples are provided to illustrate factoring, GCF, prime factorization, and finding missing factors. The document concludes with a review of the FOIL pattern for multiplying binomials.

1. 7.1 Introduction to FactoringObjectives: To find the GCF of 2 or more integers

2. To find the GCF of two or more monomials

3. To find the missing factor, given a monomial and one of its factors.Frameworks: 10.P.5

4. How could you rearrange 12 tiles to form a rectangle?

5. FactoringTo factor an integer means to express it as the product of 2 or more integers.12 = 1 x 1212 = 2 x 612 = 3 x 4

6. Factoring12 = 2 x 6 could also be expressed as12 = 2 x 3 x 2In the second case, none of the factors can be factored further without using the factor 1. 2 and 3 are called prime numbers

7. Prime NumbersA prime number is an integer greater than 1 whose only positive factors are 1 and itself.Can you think of examples?1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31

8. Composite NumbersA composite number is a positive integer that has two or more positive factors other than 1Can you think of examples?4, 6, 8, 9, 10, 12, 14, 151 is neither prime nor composite

9. Prime factorizationA factorization where all the factors are prime numbers12 = 2 x 2 x 336 = 2 x 2 x 3 x 3

10. Give the prime factorization of 90:Choose 2 positive factors of 90. Continue factoring until all the factors are prime numbers.

11. Give the prime factorization of 100:Choose 2 positive factors of 100. Continue factoring until all the factors are prime numbers.

12. Can there be more than 1prime factorization of a number?No.

13. GCF – Greatest Common FactorThe greatestcommon factor (GCF) of two or more integers is the largest integer that is a factor of all the integers.

14. Find the GCF of 72 and 8472 = 12 * 6 =84 = 14 * 6 =

15. Find the GCF of 36 and 90

16. Find the GCF of 12x4 and -28x3 and 120 x2

17. Find the GCF of 84y3and -96y6and -196y5

18. To find a missing factor, divide.For example, x3 * ____ = x7 x7 x3So, the answer is x4

19. Find the missing factor:a5 * ____ = a9___ * 5a = -30a103a3b5 * ____ = 24a4b7

20. Do p. 246 1-21

22. FOIL Review(x + 3)(x + 5)First terms: x and x x2Outside terms: x and 5 5xInside terms: 3 and x 3xLast terms: 3 and 5 15Answer: x2 + 8x + 15

23. FOIL pattern . . .

24. Homework