Factor ax^2 + bx + c

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   To split the middle of 6x² − x − 2, Milo needs two numbers that multiply to 6 × (−2) and add to −1. Type them like 1, -9. What are they?

   3, -4
2. 2.

   Noah splits the middle piece of 2x² + x − 6: two numbers that multiply to 2 × (−6) and add to 1. Type them like 1, -9. What are they?

   4, -3
3. 3.

   Pia wants two numbers that multiply to 3 × (−8) and add to 2, to split 3x² + 2x − 8. Type them like 1, -9. What are they?

   6, -4
4. 4.

   Tala wants to factor 3x² − 7x − 6. Which answer is right?

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

   Ari tries four pairs of sides for 5x² − 14x − 3. Which one is right?

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

   Bo needs the sides of 4x² + 5x − 6 for a puzzle. Which is 4x² + 5x − 6 factored?

   • (4x − 3)(x + 2)
   • (4x − 1)(x + 6)
   • (4x + 3)(x − 2)
   • (4x + 2)(x − 3)
7. 7.

   Esme has one side of 2x² − x − 15: 2x² − x − 15 = (2x + 5)(x + ▢). It may be negative. What number goes in the box?

   -3
8. 8.

   Jun has one side of 3x² + 13x − 10: 3x² + 13x − 10 = (3x − 2)(x + ▢). It may be negative. What number goes in the box?

   5
9. 9.

   Kira has one side of 4x² − 17x + 15: 4x² − 17x + 15 = (4x − 5)(x + ▢). It may be negative. What number goes in the box?

   -3
10. 10.

    Luz has one side of 5x² − 18x − 8: 5x² − 18x − 8 = (5x + 2)(x + ▢). It may be negative. What number goes in the box?

    -4