Solve cubic and quartic equations by factoring

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Ren solves x⁴ + 5x² − 36 = 0 on a math club card. What are all the real solutions?

   -2, 2
2. 2.

   Tala's robot solves x⁴ − 12x² − 64 = 0 as a quadratic in x². What are all the real solutions?

   -4, 4
3. 3.

   Zee solves x⁴ − 24x² − 25 = 0 on graph paper. What are all the real solutions?

   -5, 5
4. 4.

   Esme factors 3x⁴ − 81x = 0 using a difference of cubes. How many real solutions does it have?

   2
5. 5.

   Jun's robot factors x⁴ + 8x = 0 using a sum of cubes. How many real solutions does it have?

   2
6. 6.

   Kira factors x⁵ − 81x = 0 on graph paper. How many real solutions does it have?

   3
7. 7.

   Luz factors x⁵ − 16x = 0 in a notebook. How many real solutions does it have?

   3
8. 8.

   Milo solves x³ + 7x² = 16x + 112 on a puzzle card. What is the largest solution?

   4
9. 9.

   Noah's robot solves x³ + 9x² = 25x + 225. What is the largest solution?

   5
10. 10.

    Ren solves x³ + 8x² = 36x + 288 on graph paper. What is the largest solution?

    6