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Polynomials practice questions

25 questions from the electrical apprenticeship aptitude practice test.

Polynomials practice test

10 questions, graded as you go, with the reason for every answer. No sign-up.

What this covers

Sample questions

Add: (3x² + 2x − 5) + (x² − 6x + 9)

  1. 4x² + 8x + 4
  2. 4x² − 4x + 4
  3. 3x⁴ − 4x + 4
  4. 4x² − 4x − 14
Show the answer

B. 4x² − 4x + 4

Add like terms: 3x² + x² = 4x², 2x − 6x = −4x, and −5 + 9 = 4. Adding x² terms does not raise the exponent, so 3x⁴ is not correct.

Reference: Adding polynomials

Subtract: (5x² − 3x + 2) − (2x² + 4x − 6)

  1. 3x² + x − 4
  2. 3x² − 7x − 4
  3. 7x² + x − 4
  4. 3x² − 7x + 8
Show the answer

D. 3x² − 7x + 8

Change the sign of every term in the second polynomial, then combine: 5x² − 2x² = 3x², −3x − 4x = −7x, 2 + 6 = 8. The answer 3x² + x − 4 subtracts only the first term and adds the rest.

Reference: Subtracting polynomials

Multiply: 3x(2x − 5)

  1. 6x² − 15
  2. 6x² − 5
  3. 5x² − 15x
  4. 6x² − 15x
Show the answer

D. 6x² − 15x

Multiply 3x by each term inside: 3x × 2x = 6x² and 3x × (−5) = −15x. The answer 6x² − 5 distributes to the first term only.

Reference: Distributive property; monomial times binomial

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