Factor ax^2 + bx + c

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 1.

   Milo cuts the middle piece of 2x² + 7x + 6 in two. The numbers multiply to 2 × 6 = 12 and add to 7. Type them like 1, -9. What are they?

   4, 3
2. 2.

   Noah splits the middle of 3x² + 13x + 12 into two pieces. Their numbers multiply to 3 × 12 = 36 and add to 13. Type them like 1, -9. What are they?

   9, 4
3. 3.

   Pia splits the middle piece of 3x² + 11x + 10. The two numbers multiply to 3 × 10 = 30 and add to 11. Type them like 1, -9. What are they?

   6, 5
4. 4.

   Ren cuts the middle of 2x² + 11x + 12 into two pieces. The numbers multiply to 2 × 12 = 24 and add to 11. Type them like 1, -9. What are they?

   8, 3
5. 5.

   Zee draws 2x² + 11x + 15 as a rectangle with one side (2x + 5): 2x² + 11x + 15 = (2x + 5)(x + ▢). What number goes in the box?

   3
6. 6.

   Bo fills in the last side: 2x² + 15x + 28 = (2x + 7)(x + ▢). What number goes in the box?

   4
7. 7.

   Esme tries sides for 5x² + 17x + 6. Which is 5x² + 17x + 6 factored?

   • (5x + 3)(x + 2)
   • (5x + 1)(x + 6)
   • (5x − 2)(x − 3)
   • (5x + 2)(x + 3)
8. 8.

   Jun needs the sides of a rug of 2x² + 13x + 20 square units. Which is 2x² + 13x + 20 factored?

   • (2x + 4)(x + 5)
   • (2x + 5)(x + 4)
   • (2x − 5)(x − 4)
   • (2x + 1)(x + 20)
9. 9.

   Kira builds 3x² + 19x + 20 out of tiles. Which pair of sides fits?

   • (3x + 4)(x + 5)
   • (3x + 2)(x + 10)
   • (3x + 5)(x + 4)
   • (3x − 4)(x − 5)
10. 10.

    Luz checks four answers for 2x² + 17x + 21. Which is 2x² + 17x + 21 factored?

    • (2x + 3)(x + 7)
    • (2x + 7)(x + 3)
    • (2x − 3)(x − 7)
    • (2x + 1)(x + 21)