3. Martin-Gay, Beginning Algebra, 5ed 33

4. 44

5. 55 Find the GCF of each list of numbers. 1)6, 8 and 46 6 = 2 · 3 8 = 2 · 2 · 2 46 = 2 · 23 Example:

6. Martin-Gay, Beginning Algebra, 5ed 66 Find the GCF of each list of numbers. 1)6, 8 and 46 6 = 2 · 3 8 = 2 · 2 · 2 46 = 2 · 23 So the GCF is 2. 2)144, 256 and 300 144 = 2 · 2 · 2 · 2 · 3 · 3 256 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 300 = 2 · 2 · 3 · 5 · 5 So the GCF is 2 · 2 = 4. Example:

7. Martin-Gay, Beginning Algebra, 5ed 77 Find the GCF of each list of numbers. 1)6, 8 and 46 6 = 2 · 3 8 = 2 · 2 · 2 46 = 2 · 23 So the GCF is 2. 2)144, 256 and 300 144 = 2 · 2 · 2 · 2 · 3 · 3 256 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 300 = 2 · 2 · 3 · 5 · 5 Example:

8. Martin-Gay, Beginning Algebra, 5ed 88 Find the GCF of each list of numbers. 1)6, 8 and 46 6 = 2 · 3 8 = 2 · 2 · 2 46 = 2 · 23 So the GCF is 2. 2)144, 256 and 300 144 = 2 · 2 · 2 · 2 · 3 · 3 256 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 300 = 2 · 2 · 3 · 5 · 5 So the GCF is 2 · 2 = 4. Example:

9. Martin-Gay, Beginning Algebra, 5ed 99 Find the GCF of each list of numbers. Example: 1) x 3 and x 7 x 3 = x · x · x x 7 = x · x · x · x · x · x · x

10. Martin-Gay, Beginning Algebra, 5ed 10 Find the GCF of each list of numbers. Example: 1) x 3 and x 7 x 3 = x · x · x x 7 = x · x · x · x · x · x · x So the GCF is x · x · x = x 3 2) 6x 5 and 4x 3 6x 5 = 2 · 3 · x · x · x · x · x 4x 3 = 2 · 2 · x · x · x

11. Martin-Gay, Beginning Algebra, 5ed 11 Find the GCF of each list of numbers. Example: 1) x 3 and x 7 x 3 = x · x · x x 7 = x · x · x · x · x · x · x So the GCF is x · x · x = x 3 2) 6x 5 and 4x 3 6x 5 = 2 · 3 · x · x · x · x · x 4x 3 = 2 · 2 · x · x · x So the GCF is 2 · x · x · x = 2x 3

12. Martin-Gay, Beginning Algebra, 5ed 12 Find the GCF of each list of numbers. Example: a 3 b 2, a 2 b 5 and a 4 b 7 a 3 b 2 = a · a · a · b · b a 2 b 5 = a · a · b · b · b · b · b a 4 b 7 = a · a · a · a · b · b · b · b · b · b · b

13. Martin-Gay, Beginning Algebra, 5ed 13 Find the GCF of each list of numbers. Example: a 3 b 2, a 2 b 5 and a 4 b 7 a 3 b 2 = a · a · a · b · b a 2 b 5 = a · a · b · b · b · b · b a 4 b 7 = a · a · a · a · b · b · b · b · b · b · b So the GCF is a · a · b · b = a 2 b 2 Notice that the GCF of terms containing variables will use the smallest exponent found amongst the individual terms for each variable.

14. Martin-Gay, Beginning Algebra, 5ed 14 The First Step in factoring a polynomial is to find the GCF of all its terms.

15. Martin-Gay, Beginning Algebra, 5ed 15 Factor out the GCF in each of the following polynomials. 1)6x 3 – 9x 2 + 12x = 3x (2x 2 – 3x + 4) 2) 14x 3 y + 7x 2 y – 7xy = 7xy (2x 2 + x – 1) Example: GCF is 3x GCF is 7xy 3) 6(x + 2) – y(x + 2) = 6 · (x + 2) – y · (x + 2) = (x + 2) (6 – y) 4) xy(y + 1) – (y + 1) = xy · (y + 1) – 1 · (y + 1) = (y + 1) (xy – 1) GCF is x + 2 GCF is y + 1

16. Martin-Gay, Beginning Algebra, 5ed 16 a) b)