Lesson 38: Simplifying Expressions Using the GCF — Practice Questions

1. 1. What is the greatest common factor (GCF) of the terms in the polynomial $15x^4y^2 + 25x^2y^5$? The GCF is ___.

2. 2. Which expression is the greatest common factor of the polynomial $20m^5n^2 - 30m^3n^3$?

   • A. $10m^3n^2$
   • B. $10m^5n^3$
   • C. $60m^3n^2$
   • D. $5m^2n$

3. 3. Find the greatest common factor (GCF) for the polynomial $8a^4b^2 + 12a^3b^3 - 20a^2b^4$. The GCF is ___.

4. 4. What is the greatest common factor of the polynomial $9x^3y + 12x^2z$?

   • A. $3x^2$
   • B. $3x^2yz$
   • C. $3x^3$
   • D. 3

5. 5. What is the GCF of the terms in the expression $49p^4q^2 - 21p^6q$? The GCF is ___.

6. 6. Factor the polynomial completely by finding the greatest common factor: $20a^5 - 30a^4 + 10a^3 = 10a^3(\_\_\_)$.

7. 7. Which of the following is the correctly factored form of the expression $18m^3n^2 + 24m^2n^4$?

   • A. $6m^2n^2(3m + 4n^2)$
   • B. $6m^2n(3mn + 4n^3)$
   • C. $3m^2n^2(6m + 8n^2)$
   • D. $6mn(3m^2n + 4mn^3)$

8. 8. What is the greatest common factor (GCF) of all the terms in the polynomial $16x^5y^2 - 24x^3y^4 + 8x^3y^2$?

   • A. $8x^3y^2$
   • B. $4x^3y^2$
   • C. $8x^5y^4$
   • D. 8

9. 9. Factor the polynomial completely: $28x^4 - 35x^3 + 7x^2 = \_\_\_$.

10. 10. Which expression shows $14a^2b^3 - 21a^3b^2$ correctly factored?

    • A. $7a^2b^2(2b - 3a)$
    • B. $7ab(2ab^2 - 3a^2b)$
    • C. $7a^2b^2(2b - 3)$
    • D. $14a^2b^2(b - 2a)$