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Question

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consider the polynomial ( 3x^3 - 2x + 7 ).

  1. how many terms does this polynomial have?
  2. what is the coefficient of the second term?
  3. the polynomial has five terms.
  4. the coefficient of the second term is ( -2 ).
  5. the polynomial has five terms.
  6. the coefficient of the second term is ( x ).
  7. the polynomial has three terms.
  8. the coefficient of the second term is ( -2 ).
  9. the polynomial has three terms.
  10. the coefficient of the second term is ( x ).

Explanation:

Brief Explanations
  1. For the number of terms in the polynomial \(3x^{3}-2x + 7\), we identify the terms separated by addition or subtraction: \(3x^{3}\), \(-2x\), and \(7\). So there are 3 terms.
  2. The second term is \(-2x\). The coefficient of a term is the numerical factor. So the coefficient of \(-2x\) is \(-2\).

Looking at the options, the correct one is the third option (the one with "1) The polynomial has three terms. 2) The coefficient of the second term is \(-2\)").

Answer:

  1. The polynomial has three terms.
  2. The coefficient of the second term is \(-2\). (The option with these two statements)