Greatest common factor of monomials, and pulling it out

Answer Key - Grade 9 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. Read this first

   Factor strips

   12x³y = 2 · 2 · 3 · x · x · x · y; 18x²y² = 2 · 3 · 3 · x · x · y · y.

2. 1.

   Ari lines up the factor strips for 12x³y and 18x²y², like two trains side by side. Type powers like x^2. What is their greatest common factor (GCF)?

   6x^2y

3. Factor strips

   10x⁴y² = 2 · 5 · x · x · x · x · y · y; 15x²y³ = 3 · 5 · x · x · y · y · y.

4. 2.

   Bo writes out the factor strips for 10x⁴y² and 15x²y³. Type powers like x^2. What is their greatest common factor (GCF)?

   5x^2y^2

5. Factor strips

   8xy³ = 2 · 2 · 2 · x · y · y · y; 20x²y² = 2 · 2 · 5 · x · x · y · y.

6. 3.

   Esme compares the factor strips for 8xy³ and 20x²y². Type powers like x^2. What is their greatest common factor (GCF)?

   4xy^2
7. 4.

   Kira draws 14x³y + 21x²y² as two pieces that share the side 7x²y. Type powers like y^2. What is the other side of the 21x²y² piece?

   3y
8. 5.

   Luz draws 16x⁴y² − 24x³y³ as two pieces that share the side 8x³y². Type powers like y^2. What is the other side of the 16x⁴y² piece?

   2x
9. 6.

   Milo draws 30x²y³ + 18xy as two pieces that share the side 6xy. Type powers like y^2. What is the other side of the 30x²y³ piece?

   5xy^2
10. 7.

    Noah draws 27x⁵y² + 45x³y⁴ as two pieces that share the side 9x³y². Type powers like y^2. What is the other side of the 45x³y⁴ piece?

    5y^2
11. 8.

    Pia needs the greatest common factor of 12x⁵, 18x⁴ and 30x² for a puzzle card. Which is it?

    • 6
    • 3x²
    • 6x²
    • 6x⁵
12. 9.

    Ren draws 16x⁵, 24x³ and 40x⁷ as three pieces with one shared side. Which is their greatest common factor?

    • 8
    • 4x³
    • 8x⁷
    • 8x³
13. 10.

    Tala checks a homework answer for the GCF of 18x⁶, 27x² and 45x⁴. Which is the GCF?

    • 9
    • 9x²
    • 3x²
    • 9x⁶