text: # The expression [x + (x3 - 1)½]5 + [x - (x3 - 1)½]5 is a polynomial of degree
  
  1) 5
  
  2) 6
  
  3) 7
  
  4) 8
  
  Solution: (3) 7
  
  $$\begin{array}{l}(a+b)^{5}+(a-b)^{5}\\ ={ }^{5} C_{0} a^{5}+{ }^{5} C_{1} a^{4} b+{ }^{5} C_{2} a^{3} b^{2}+{ }^{5} C_{3} a^{2} b^{3}+{ }^{5} C_{4} a b^{4}+{ }^{5} C_{5} b^{5}+{ }^{5} C_{0} a^{5}-{ }^{5} C_{1} a^{4} b +{ }^{5} C_{2} a^{3} b^{2}-{ }^{5} C_{3} a^{2} b^{3}+{ }^{5} C_{4} a b^{4}-{ }^{5} C_{5} b^{5}\\ =2\left[a^{5}+10 a^{3} b^{2}+5 a b^{4}\right]\\ \therefore \quad\left[x+\left(x^{3}-1\right)^{1 / 2}\right]^{5}+\left[x-\left(x^{3}-1\right)^{1 / 2}\right]^{5}\\ =2\left[x^{5}+10 x^{3}\left(x^{3}-1\right)+5 x\left(x^{3}-1\right)^{2}\right]\\ \text \ The \ given \ expression \ is \ a \ polynomial \ of \ degree \ 7.\end{array}$$
explanation: The document contains a math question and its corresponding solution. The question asks for the degree of the polynomial represented by the given expression, and the solution provides a detailed step-by-step expansion and simplification to determine that the degree is 7.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # The expression [x + (x3 - 1)½]5 + [x - (x3 - 1)½]5 is a polynomial of degree
  
  1) 5
  
  2) 6
  
  3) 7
  
  4) 8
  
  Solution: (3) 7
  
  $$\begin{array}{l}(a+b)^{5}+(a-b)^{5}\\ ={ }^{5} C_{0} a^{5}+{ }^{5} C_{1} a^{4} b+{ }^{5} C_{2} a^{3} b^{2}+{ }^{5} C_{3} a^{2} b^{3}+{ }^{5} C_{4} a b^{4}+{ }^{5} C_{5} b^{5}+{ }^{5} C_{0} a^{5}-{ }^{5} C_{1} a^{4} b +{ }^{5} C_{2} a^{3} b^{2}-{ }^{5} C_{3} a^{2} b^{3}+{ }^{5} C_{4} a b^{4}-{ }^{5} C_{5} b^{5}\\ =2\left[a^{5}+10 a^{3} b^{2}+5 a b^{4}\right]\\ \therefore \quad\left[x+\left(x^{3}-1\right)^{1 / 2}\right]^{5}+\left[x-\left(x^{3}-1\right)^{1 / 2}\right]^{5}\\ =2\left[x^{5}+10 x^{3}\left(x^{3}-1\right)+5 x\left(x^{3}-1\right)^{2}\right]\\ \text \ The \ given \ expression \ is \ a \ polynomial \ of \ degree \ 7.\end{array}$$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its corresponding solution. The question asks for the degree of the polynomial represented by the given expression, and the solution provides a detailed step-by-step expansion and simplification to determine that the degree is 7.
  
  Label: question-and-answer