Greatest common factor of monomials, and pulling it out

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Ari pulls out −4x², the GCF with a minus sign, from −8x⁴ + 12x³ − 4x². Type powers like x^2. What is it written as −4x² times a bracket?

   -4x^2(2x^2 - 3x + 1)
2. 2.

   Esme pulls out −5x², the GCF with a minus sign, from −10x⁵ − 25x³ + 5x². Type powers like x^2. What is it written as −5x² times a bracket?

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

   Jun pulls out −7x²y², the GCF with a minus sign, from −14x⁴y² + 21x³y³ − 7x²y². Type powers like x^2. What is it written as −7x²y² times a bracket?

   -7x^2y^2(2x^2 - 3xy + 1)
4. 4.

   Kira factors 18x⁴y² − 27x³y³ with its greatest common factor pulled out. Which answer is right?

   • 9x³y²(2x − 3y)
   • 3x³y²(6x − 9y)
   • 9x³(2xy² − 3y³)
   • 9x³y²(2x − 27x³y³)
5. 5.

   Luz and a friend each factor 20x³y⁴ + 30x²y⁵. Which answer has the greatest common factor pulled out?

   • 10x²(2xy⁴ + 3y⁵)
   • 5x²y⁴(4x + 6y)
   • 10x²y⁴(2x + 3y)
   • 10x²y⁴(2x + 30x²y⁵)
6. 6.

   Milo pulls the greatest common factor out of 24x⁵y³ − 16x²y⁴. Which answer is right?

   • 8x²y³(3x³ − 16x²y⁴)
   • 4x²y³(6x³ − 4y)
   • 8y³(3x⁵ − 2x²y)
   • 8x²y³(3x³ − 2y)
7. 7.

   Pia's quilt row has three patches of 12x³, 18x² and 30x square inches. Every patch has the same height: the GCF of the areas. How wide is the whole row?

   2x^2 + 3x + 5
8. 8.

   Ren lays three rug strips of 8x⁴, 20x³ and 12x² square feet in a row. They share one height, the GCF of the areas. How wide is the row?

   2x^2 + 5x + 3
9. 9.

   Tala sews three patches of 15x³, 10x² and 25x square inches in a row, all as tall as the GCF of the areas. How wide is the row?

   3x^2 + 2x + 5
10. 10.

    Zee cuts three paper strips of 18x⁴, 12x³ and 6x² square inches. Each is as tall as the GCF of the areas. How wide are they in a row?

    3x^2 + 2x + 1