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Factoring Higher-Degree Polynomials - Worksheet 8 - 11th Grade

Hard

Factor, evaluate and interpret polynomial expressions with checked algebraic identities.

hard: Use another set to practice explaining and checking your answers.

27 problems · 20-25 minutes · Skills: polynomials, factoring, algebra

About This Worksheet

This hard-level worksheet contains 27 problems designed for 11th Grade students practicing factoring higher-degree polynomials. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Factor polynomials, use exponent laws and solve equations with domain restrictions.

  • Factor, evaluate and interpret polynomial expressions with checked algebraic identities.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: Factor completely over the integers: x³ − 9x.
Solution Steps:
  1. Factor out the common factor x.
  2. Factor the remaining difference of squares.
Answer: x(x − 3)(x + 3)
Tip: Check your result using the method in the example before moving to the next question.
1
Factor completely over the integers: x³ − 4x.
2
Factor completely over the integers: x³ − 36x.
3
Factor completely over the integers: x³ − 25x.
4
Factor completely over the integers: x³ − 1x.
5
Factor completely over the integers: x³ − 9x.
6
Factor completely over the integers: x³ − 16x.
7
Factor completely over the integers: x³ − 25x.
8
Factor completely over the integers: x³ − 9x.
9
Factor completely over the integers: x³ − 25x.
10
Factor completely over the integers: x³ − 36x.
11
Factor completely over the integers: x³ − 1x.
12
Factor completely over the integers: x³ − 16x.
13
Factor completely over the integers: x³ − 4x.
14
Factor completely over the integers: x³ − 1x.
15
Factor completely over the integers: x³ − 4x.
16
Factor completely over the integers: x³ − 25x.
17
Factor completely over the integers: x³ − 36x.
18
Factor completely over the integers: x³ − 4x.
19
Factor completely over the integers: x³ − 9x.
20
Factor completely over the integers: x³ − 36x.
21
Factor completely over the integers: x³ − 25x.
22
Factor completely over the integers: x³ − 1x.
23
Factor completely over the integers: x³ − 25x.
24
Factor completely over the integers: x³ − 16x.
25
Factor completely over the integers: x³ − 36x.
26
Factor completely over the integers: x³ − 16x.
27
Factor completely over the integers: x³ − 25x.

Answer Key

1. x(x − 2)(x + 2)2. x(x − 6)(x + 6)3. x(x − 5)(x + 5)4. x(x − 1)(x + 1)5. x(x − 3)(x + 3)6. x(x − 4)(x + 4)7. x(x − 5)(x + 5)8. x(x − 3)(x + 3)9. x(x − 5)(x + 5)10. x(x − 6)(x + 6)11. x(x − 1)(x + 1)12. x(x − 4)(x + 4)13. x(x − 2)(x + 2)14. x(x − 1)(x + 1)15. x(x − 2)(x + 2)16. x(x − 5)(x + 5)17. x(x − 6)(x + 6)18. x(x − 2)(x + 2)19. x(x − 3)(x + 3)20. x(x − 6)(x + 6)21. x(x − 5)(x + 5)22. x(x − 1)(x + 1)23. x(x − 5)(x + 5)24. x(x − 4)(x + 4)25. x(x − 6)(x + 6)26. x(x − 4)(x + 4)27. x(x − 5)(x + 5)

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What skills does this polynomial functions worksheet cover?

This worksheet focuses on polynomials, factoring, algebra. It is designed for 11th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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How many problems are on this worksheet?

This worksheet contains 27 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.