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Grade 11–12Common Core style · Math: algebra

Polynomial Equation Worksheets — Free with Answers

Practise cubic equations: cube roots, rearranging and the zero-product property.

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Area
Algebra
Exercise type
Polynomial equations
Grade
11 (ages 16–17)
Difficulty
Easy
Number of tasks
20
Task format
Calculations
Paper size
US Letter
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Polynomial equations · Grade 11

Name: ____________________

Worked example

  1. x³ = a: take the cube root of both sides.
  2. x³ = kx: move everything to one side and factor out x, so x = 0 is one solution.
  3. (x − a)(x − b)(x − c) = 0: the zero-product property gives x = a, x = b and x = c.
Example: how to solve it
1.

Solve: x³ = 125

2.

Solve: x³ = 64

3.

Solve: x³ = 8

4.

Solve: x³ = 216

5.

Solve: x³ = 343

6.

Solve: x³ = 729

7.

Solve: x³ = 27

8.

Solve: x³ = 512

9.

Solve: x³ = 216

10.

Solve: x³ = 216

11.

Solve: x³ = 729

12.

Solve: x³ = 343

13.

Solve: x³ = 216

14.

Solve: x³ = 729

15.

Solve: x³ = 343

16.

Solve: x³ = 216

17.

Solve: x³ = 216

18.

Solve: x³ = 64

19.

Solve: x³ = 27

20.

Solve: x³ = 216

Answer key

  1. 1. x = 5
  2. 2. x = 4
  3. 3. x = 2
  4. 4. x = 6
  5. 5. x = 7
  6. 6. x = 9
  7. 7. x = 3
  8. 8. x = 8
  9. 9. x = 6
  10. 10. x = 6
  11. 11. x = 9
  12. 12. x = 7
  13. 13. x = 6
  14. 14. x = 9
  15. 15. x = 7
  16. 16. x = 6
  17. 17. x = 6
  18. 18. x = 4
  19. 19. x = 3
  20. 20. x = 6

Created with WorksheetMint

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  2. Print or save as PDF with the answer key.
  3. “Create new version” gives new numbers.

About this generator

Easy gives x³ = a with whole-number roots, medium x³ = kx with roots −r, 0 and r, and hard factored equations (x − r₁)(x − r₂)(x − r₃) = 0. The answer key is calculated by the website. No sign-up needed.

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Choose an age or grade in step 2. Start easier if the pupil is unsure – you can switch anytime and get new problems instantly.
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Turn on Answer key in the last step. It prints on its own page after the problems, with the same numbering.
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