1. Chapter 9.1

2. Factoring a number  Objective NCSCOS 1.01 – Write equivalent forms of algebraic expressions to solve problems  Students will know how to factor number and find the greatest common factor

3. Factoring a number  Prime number –  A number that can only be divided by 1 and itself  Ex. 2, 3, 5, 7, 11, 13  Composite number –  A number that can be divided by more than 1 and itself  Ex. 4: (1*4, 2*2)  Ex. 6: (1*6, 2*3)

4. Factoring a number  Prime Factorization –  A composite number expressed as a product of factors that are all prime numbers  The process of factoring a number down to only prime numbers

5. Factoring a number  Label the following as prime or composite  24  23  18  9  53

6. Factoring a number  Label the following as prime or composite  24  23  18  9  53 Composite Prime Composite Prime

7. Factoring a number  Example 1: Find the prime factorization of 90  The smallest prime number is 2, so we start with 2  When you take a 2 out, you’re left with 45

8. Factoring a number  Example 1: Find the prime factorization of 90  The two numbers below 90 should multiply to the number above it  2 can’t be factored any more, so we’ll have to factor the 45 more x = 90

9. Factoring a number  Example 1: Find the prime factorization of 90  The next smallest prime number is 3, so take 3 out of 45  Notice that 3 and 15 multiply to the number above it x = 45

10. Factoring a number  Example 1: Find the prime factorization of 90  15 can be factored by 3 again  At this point, all the number are prime

11. Factoring a number  Example 1: Find the prime factorization of 90  We can multiply all these numbers together to get 90

12. Factoring a number  Example 1: Find the prime factorization of 90  We can then write 3 * 3 as 3 2  We now have 90 fully factored

13. Factoring a number  Example 2: Factor -28  If it’s negative, factor out -1 first  Now factor a positive 28

14. Factoring a number  Factor the following numbers: 1. 24 3. -110 5. 210 4. 168 2. 36

15. Factoring a number  Factor the following numbers: 1. 24 3. -110 5. 210 4. 168 2. 36 2 * 3 * 5 * 7 2 3 * 3 2 2 * 3 2 -1 * 2 * 5 * 11 2 3 * 3 * 7

16. Factoring a number  Example 3: Factor  Factor the number first

17. Factoring a number  Example 3: Factor  Then factor the variable  Remember, x 3 is x*x*x

18. Factoring a number  Example 3: Factor  We can now reduce this to get our answer

19. Factoring a number  Factor the following: 1. 20x 2 3. -120x 3 5. 252x 4 y 2 4. 68x 3 y 5 2. 32x 5

20. Factoring a number  Factor the following: 1. 20x 2 3. -120x 3 5. 252x 4 y 2 4. 68x 3 y 5 2. 32x 5 2 2 * 5 * x 2 2 5 * x 5 -1 * 2 3 * 3 * 5 * x 3 2 2 * 17 * x 3 * y 5 2 2 * 3 3 * 7 * x 4 *y 2

21. Factoring a number  Example 4:Find the Greatest Common Factor of :  We need to factor both numbers first and

22. Factoring a number  Factor 24

23. Factoring a number  Factor 36

24. Factoring a number  Write out each numbers factors  Find what they have in common  Multiply what they have in common to find the Greatest Common Factor GCF

25. Factoring a number  Find the GCF for:  Factor each number first  Find what they have in common and

26. Factoring a number  Find the GCF for:  Factor each number first  Find what they have in common and

27. Factoring a number  Find the GCF for:  You have to factor the numbers to find the GCF but you can use a shortcut for the variables:  Which value of x has the lowest number as an exponent will be your GCF and

28. Factoring a number  Find the Greatest Common Factor for the following: 1. 12 and 162. 120 and 180 3. 54x 3 and 90x 5 5. 312x 5 and 468x 7 4. 52x 4 and 104x 4

29. Factoring a number  Find the Greatest Common Factor for the following: 1. 12 and 162. 120 and 180 3. 54x 3 and 90x 5 18x 3 60 4 26x 4 4. 52x 4 and 104x 4 5. 312x 5 and 468x 7 156x 5

30. Factoring a number  Example: Find the GCF for the following numbers:  First, factor out each number

31. Factoring a number  Find what they have in common  They all have one 2  They also have one 3

32. Factoring a number  Multiply the numbers  Find the smallest value of x and plug it in

33. Factoring a number  Example: Find the GCF for the following numbers:  The answer is:

34. Factoring a number  Factor: 252  Factor: -594x 2 y 4  Find the greatest common factor:  48 and 120  84x 5 and 112x 3  117x 7, 468x 4 and 351x 5

35. Factoring a number  Factor: 252  Factor: -594x 2 y 4  Find the greatest common factor:  48 and 120  84x 5 and 112x 3  117x 7, 468x 4 and 351x 5 2 2 *3 2 *7 -1*2*3 3 *11*x 2 *y 4 24 28x 3 117x 4