Solve cubic and quartic equations by factoring

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   Kira writes x(x − 4)(x + 7) = 0 on a math club card. Which list gives every solution?

   • -7 and 4
   • -7, 0 and 4
   • -4, 0 and 7
2. 2.

   Luz's robot solves (x + 2)(x − 5)(x − 8) = 0 by setting each factor to 0. Which list gives every solution?

   • -8, -5 and 2
   • -2, 5 and 8
   • 2, 5 and 8
3. 3.

   Milo solves x²(x + 3) = 0 on graph paper. Which list gives every solution?

   • -3
   • -3 and 0
   • 0 and 3, with the sign flipped
4. 4.

   Table with an empty output column for y = x³ − 7x + 6; inputs -2, 0, 2, 6. Ren tests numbers in x³ − 7x + 6 = 0 with a table. Which number is a solution?

   • 2
   • -2
   • 0
   • 6

5. Read this first

   Use this

   Table with an empty output column for y = x³ − 3x² − 4x + 12; inputs -3, 0, 3, 12.

6. 5.

   Zee substitutes numbers into x³ − 3x² − 4x + 12 = 0. Which number is a solution?

   • 3
   • -3
   • 12
   • 0
7. 6.

   Table with an empty output column for y = x⁴ − 5x² + 4; inputs -2, 0, 3, 4. Bo checks numbers in x⁴ − 5x² + 4 = 0 using a table. Which number is a solution?

   • 4
   • 0
   • -2
   • 3
8. 7.

   Esme factors x³ − 7x² + 12x as x(x² − 7x + 12). What are all the solutions of x³ − 7x² + 12x = 0?

   0, 3, 4
9. 8.

   Jun's robot factors x³ + 9x² + 20x as x(x² + 9x + 20). What are all the solutions of x³ + 9x² + 20x = 0?

   -5, -4, 0
10. 9.

    Kira factors 2x³ − 6x² − 20x as 2x(x² − 3x − 10). What are all the solutions of 2x³ − 6x² − 20x = 0?

    -2, 0, 5
11. 10.

    Luz factors x³ − 11x² + 30x as x(x² − 11x + 30). What are all the solutions of x³ − 11x² + 30x = 0?

    0, 5, 6