Solve cubic and quartic equations by factoring

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Milo groups the terms of x³ + 2x² − 9x − 18 = 0 on a puzzle card. What are all the solutions?

   -3, -2, 3
2. 2.

   Noah's robot factors x³ − 5x² − 4x + 20 = 0 by grouping. What are all the solutions?

   -2, 2, 5
3. 3.

   Ren solves x³ + 3x² − 16x − 48 = 0 by grouping. What are all the solutions?

   -4, -3, 4
4. 4.

   Tala groups x³ − x² − 25x + 25 = 0 in a notebook. What are all the solutions?

   -5, 1, 5
5. 5.

   Zee treats x² as one letter to solve x⁴ − 13x² + 36 = 0. What are all the solutions?

   -3, -2, 2, 3
6. 6.

   Bo's robot solves x⁴ − 10x² + 9 = 0 as a quadratic in x². What are all the solutions?

   -3, -1, 1, 3
7. 7.

   Jun solves x⁴ − 29x² + 100 = 0 by factoring it like a quadratic. What are all the solutions?

   -5, -2, 2, 5
8. 8.

   Kira solves 2x³ − 18x = 0 on a puzzle card. Which list gives every solution?

   • 0 and 9
   • -3, 0 and 3
   • 0 and 3
   • -3 and 3, after dividing by x
9. 9.

   Milo solves 4x³ − 100x = 0 on graph paper. Which list gives every solution?

   • -5 and 5, after dividing by x
   • -5, 0 and 5
   • 0 and 5
   • 0 and 25
10. 10.

    Noah solves 5x⁴ − 20x² = 0 in a notebook. Which list gives every solution?

    • 0 and 2
    • -2, 0 and 2
    • -2 and 2
    • 0 and 4