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.

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

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

   Noah marks the zero rows for (x + 6)(x − 1)(x + 9) = 0 on a grid map. Which list gives every solution?

   • -1, 6 and 9
   • -9, 1 and 6
   • -9, -6 and 1
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
   • 0
   • 6
   • 2

5. Read this first

   Use this

   Table with an empty output column for y = x³ + 2x² − 5x − 6; inputs -6, -3, 0, 3.

6. 5.

   Tala's robot tests inputs in x³ + 2x² − 5x − 6 = 0. Which number is a solution?

   • -6
   • -3
   • 0
   • 3

7. Use this

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

8. 6.

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

   • 0
   • -3
   • 12
   • 3
9. 7.

   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?

   • 0
   • -2
   • 4
   • 3
10. 8.

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

    0, 3, 4
11. 9.

    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
12. 10.

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

    -2, 0, 5