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Assignment: Simplify Using Greatest Common Factor (GCF) For each rational expression, identify the greatest common factor (GCF), write the expression in factored form, and simplify. Show all work leading to your answer.

1. 4

3

27

3

a

a

2. 5

2 6

15

25

m n

m n

3. 4 6

3

x x

x

4. 5

9 4

a

a a

5. 2

4

3

5

b b

b

6. 2 3 2 2

3 4

9

2

x y x y

x y

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7. 3

4 2

21

7 14

y

y y

8. 4 3 2

2

6 12 3

9

x x x

x

9. 5 3

3 4 5 3

2 10

4 12

p q pq

p q p q

10. Imagine you are trying to help another Algebra 1 student learn how to simplify rational

expressions using the GCF. To help the student, write your own example of a rational

expression and demonstrate how to simplify the expression using the GCF.

a. Write a rational expression with a GCF that has both a numeric part and a

variable part.

b. Identify the GCF and show how you can simplify your rational expression using

the GCF.

c. To help the student remember the procedure, write 2-3 sentences describing

how you simplified your rational expression using the GCF.

topmostSubform[0]: Page1[0]: TextField1[0]: GCF of 27 and 3 is 3.GCF of 4 and 3 is a or 1. Answer: 3aTextField1[1]: GCF of 15 and 25 is 5.GCF of 5 and 2 is m or 1.GCF of 1 and 6 is n or 1.Answer: 5mnTextField1[2]: GCF is 3.Answer: x^6 + x ----------- x TextField1[3]: GCF is 4. Answer: a^4 ------- a^5 - aTextField1[4]: GCF is 1.Answer: 3^5 + 3b^2 ---------------- 5TextField1[5]: GCF of 9 and 2 is 2. GCF of 2 and 3 is 2. GCF of 4 and 2 is 2. Answer: x^2y^3(18+x^3y^3) ------------------------- 2

Page2[0]: TextField1[0]: GCF is 2. Answer: 3y^y - 14y^2TextField1[1]: GCF of 6, 12, 3, 9 is 3. GCF od 4, 3, 2, 2 is 2. Answer: 17x^4 --------- + 12x^3 3TextField1[2]: Answer: 12p^5q^3 + 2q^5 - 5/2p^4q^7TextField1[3]: x^3y^2 - xy

TextField1[4]: GCF: 3x(2x + 1)TextField1[5]: After i got the gcf, I looked at the other parts of the expression. Then I pulled out the gcf from each term to make it easier.