Solve a quadratic by factoring (zero product property)

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Kira's robot solves 3x² - 10x - 8 = 0 and asks for a fraction. It factors as (3x + 2)(x - 4) = 0. What is the negative solution?

   -2/3
2. 2.

   Luz solves 4x² + 4x - 15 = 0 with a sharp pencil. It factors as (2x - 3)(2x + 5) = 0. What is the positive solution?

   3/2
3. 3.

   In math club, Milo solves 5x² - 13x - 6 = 0. It factors as (5x + 2)(x - 3) = 0. What is the negative solution?

   -2/5
4. 4.

   Noah's puzzle card says x(x - 5) = 36. What is the larger solution?

   9
5. 5.

   Pia solves (x + 2)(x + 5) = 28 (it looks friendly, but there is a trap). What is the smaller solution?

   -9
6. 6.

   Ren's robot solves (x - 1)(x + 6) = 30. What is the larger solution?

   4
7. 7.

   Zee's puzzle card says x² - 10x + 25 = 0. Which gives every solution?

   • x = 5 or x = -5
   • x = -5 only
   • x = 5 only
   • No real solution
8. 8.

   Ari solves x² + 14x + 49 = 0 in pencil. Which gives every solution?

   • x = -7 only
   • No real solution
   • x = -7 or x = 7
   • x = 7 only
9. 9.

   Bo's robot solves 4x² + 12x + 9 = 0 and wants a fraction. Which gives every solution?

   • x = 3/2 only
   • x = -3/2 or x = 3/2
   • x = -3/2 only
   • x = -3 only
10. 10.

    Esme's math book shows 9x² - 24x + 16 = 0. Which gives every solution?

    • x = -4/3 only
    • x = 4 only
    • x = 4/3 only
    • x = 4/3 or x = -4/3