Greatest common factor of monomials, and pulling it out

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Ari has three tiles with areas 24x⁴y², 36x³y³ and 60x²y⁵. Type powers like x^2. What is their greatest common factor?

   12x^2y^2
2. 2.

   Esme is stuck on a card that lists 20xy⁴, 32x³y² and 44x²y³. Type powers like x^2. What is their greatest common factor?

   4xy^2
3. 3.

   Jun lines up pieces with areas 45x⁶y³, 75x⁴y⁴ and 90x⁵y². Type powers like x^2. What is their greatest common factor?

   15x^4y^2
4. 4.

   Kira factors 15x³y² − 10x²y² + 5x²y by pulling out the greatest common factor. Type powers like x^2. What is it written as the GCF times a bracket?

   5x^2y(3xy - 2y + 1)
5. 5.

   Luz factors 12x⁴y + 8x³y² + 4x²y by pulling out the greatest common factor. Type powers like x^2. What is it written as the GCF times a bracket?

   4x^2y(3x^2 + 2xy + 1)
6. 6.

   Noah factors 14x⁵y² + 35x⁴y² − 21x³y³ by pulling out the greatest common factor. Type powers like x^2. What is it written as the GCF times a bracket?

   7x^3y^2(2x^2 + 5x - 3y)
7. 7.

   Pia wants the least common multiple (LCM) of 6x²y and 8xy³. Type powers like x^2. What is the LCM?

   24x^2y^3
8. 8.

   Ren needs the smallest monomial that both 4x³y² and 10x²y⁵ divide into. Type powers like x^2. What is their LCM?

   20x^3y^5
9. 9.

   Tala finds the least common multiple (LCM) of 9xy⁴ and 12x³y for a puzzle. Type powers like x^2. What is it?

   36x^3y^4
10. 10.

    Zee checks a classmate's LCM of 15x⁴y and 25x²y³. Type powers like x^2. What is the LCM?

    75x^4y^3