Finding the Value of n in a Polynomial Product
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Questions and Answers

If the sum of the coefficients of all even powers of $x$ in the product is 61, what is the value of $n$?

  • 8 (correct)
  • 9
  • 10
  • 7
  • What is the sum of the coefficients of all even powers of $x$ in the product $(1 + x + x^2 + … + x^{2n}) (1 – x + x^2 – x^3 + … + x^{2n})$?

  • $n^2$
  • $2n^2 - 1$ (correct)
  • $2n^2 + 1$
  • 2n + 1
  • What is the coefficient of $x^{10}$ in the product $(1 + x + x^2 + … + x^{20}) (1 – x + x^2 – x^3 + … + x^{20})$?

  • -19 (correct)
  • -17
  • -16
  • -18
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