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Factoring Polynomials

Test your understanding of factoring polynomials by solving the following questions.

14 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Factor the polynomial (x^2 + 5x + 6).

  1. (x + 2)(x + 3)
  2. (x - 2)(x - 3)
  3. (x + 1)(x + 6)
  4. (x - 1)(x - 6)
Question 2 Multiple Choice (Single Answer)

Factor the polynomial (x^2 - 9).

  1. (x + 3)(x - 3)
  2. (x + 9)(x - 9)
  3. (x + 1)(x - 9)
  4. (x - 1)(x + 9)
Question 3 Multiple Choice (Single Answer)

Factor the polynomial (x^2 - 4x + 4).

  1. (x + 2)^2
  2. (x - 2)^2
  3. (x + 4)(x - 4)
  4. (x - 4)(x + 4)
Question 4 Multiple Choice (Single Answer)

Factor the polynomial (x^3 + 2x^2 + x).

  1. x(x + 1)^2
  2. x(x - 1)^2
  3. x(x + 2)(x - 1)
  4. x(x - 2)(x + 1)
Question 5 Multiple Choice (Single Answer)

Factor the polynomial (x^3 - 8).

  1. (x - 2)(x^2 + 2x + 4)
  2. (x + 2)(x^2 - 2x + 4)
  3. (x - 2)^3
  4. (x + 2)^3
Question 6 Multiple Choice (Single Answer)

Factor the polynomial (x^4 - 16).

  1. (x^2 + 4)(x^2 - 4)
  2. (x^2 + 2)(x^2 - 8)
  3. (x + 2)^2(x - 2)^2
  4. (x - 2)^4
Question 7 Multiple Choice (Single Answer)

Factor the polynomial (x^5 - 32).

  1. (x - 2)(x^4 + 2x^3 + 4x^2 + 8x + 16)
  2. (x + 2)(x^4 - 2x^3 + 4x^2 - 8x + 16)
  3. (x - 2)^5
  4. (x + 2)^5
Question 8 Multiple Choice (Single Answer)

Factor the polynomial (x^6 - 64).

  1. (x^3 + 4)(x^3 - 16)
  2. (x^3 + 8)(x^3 - 8)
  3. (x^2 + 8)(x^4 - 8x^2 + 64)
  4. (x^2 - 8)(x^4 + 8x^2 + 64)
Question 9 Multiple Choice (Single Answer)

Factor the polynomial (x^8 - 1).

  1. (x^4 + 1)(x^4 - 1)
  2. (x^2 + 1)(x^6 - x^4 + x^2 - 1)
  3. (x^2 - 1)(x^6 + x^4 + x^2 + 1)
  4. (x + 1)(x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)
Question 10 Multiple Choice (Single Answer)

Factor the polynomial (x^{10} - 1).

  1. (x^5 + 1)(x^5 - 1)
  2. (x^2 + 1)(x^8 - x^6 + x^4 - x^2 + 1)
  3. (x^2 - 1)(x^8 + x^6 + x^4 + x^2 + 1)
  4. (x + 1)(x^9 - x^8 + x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)
Question 11 Multiple Choice (Single Answer)

Factor the polynomial (x^3 + 3x^2 + 3x + 1).

  1. (x + 1)^3
  2. (x - 1)^3
  3. (x + 1)(x^2 - x + 1)
  4. (x - 1)(x^2 + x + 1)
Question 12 Multiple Choice (Single Answer)

Factor the polynomial (x^3 - 3x^2 + 3x - 1).

  1. (x - 1)^3
  2. (x + 1)^3
  3. (x - 1)(x^2 + x + 1)
  4. (x + 1)(x^2 - x + 1)
Question 13 Multiple Choice (Single Answer)

Factor the polynomial (x^4 + 6x^2 + 9).

  1. (x^2 + 3)^2
  2. (x^2 - 3)^2
  3. (x + 3)^2(x - 3)^2
  4. (x^2 + 9)(x^2 - 9)
Question 14 Multiple Choice (Single Answer)

Factor the polynomial (x^4 - 6x^2 + 9).

  1. (x^2 + 3)^2
  2. (x^2 - 3)^2
  3. (x + 3)^2(x - 3)^2
  4. (x^2 + 9)(x^2 - 9)
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