Divide a polynomial by a monomial or by a binomial

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 1.

   Ren draws a rectangle of area 12x³ + 18x² with one side 6x. Divide each piece by 6x. Type powers like x^2. What is the other side?

   2x^2 + 3x
2. 2.

   Tala's tile pattern has area 6x⁴ − 9x³ + 3x² and one side 3x². Divide each piece by 3x². Type powers like x^2. What is the other side?

   2x^2 - 3x + 1
3. 3.

   Zee's quilt has area 20x³ + 8x² − 4x and one side 4x. Divide each piece by 4x. Type powers like x^2. What is the other side?

   5x^2 + 2x - 1
4. 4.

   Bo draws a rectangle of area x² − 3x − 28 with one side x − 7. The other side is x + ▢. It may be negative. What number goes in the box?

   4
5. 5.

   Esme's window has area x² − 5x − 24 and one side x + 3. The other side is x + ▢. It may be negative. What number goes in the box?

   -8
6. 6.

   Jun's rug has area x² − 11x + 30 and one side x − 6. The other side is x + ▢. It may be negative. What number goes in the box?

   -5
7. 7.

   Kira divides 20x³ − 12x² by 4x, using an area model. Which answer is right?

   • 5x² − 3x
   • 5x³ − 3x²
   • 5x⁴ − 3x³
   • 5x² − 12x²
8. 8.

   Luz finds the missing side when the area is 18x⁴ + 27x² and one side is 9x². Which answer is right?

   • 2x⁴ + 3x²
   • 2x⁶ + 3x⁴
   • 2x² + 3
   • 2x² + 27x²
9. 9.

   Milo checks a friend's work on (24x³ + 16x) ÷ 8x. Which answer is right?

   • 3x² + 2
   • 3x⁴ + 2x²
   • 3x³ + 2x
   • 3x² + 16x
10. 10.

    Noah splits the area 35x⁵ − 10x³ into pieces with one side 5x³. Which is the other side?

    • 7x⁸ − 2x⁶
    • 7x² − 2
    • 7x² − 10x³
    • 7x⁵ − 2x³