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For the polynomials in the following exercise, state the degree and the number of terms, and describe the long-run behavior.

y=12x4+x3y=1-2 x^4+x^3


Answered 2 years ago
Answered 2 years ago
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Recall: The standard form of the general formula for a polynomial function is

p(x)=anxn+an1xn1+...+a1x+a0,an0p(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{1}x+a_{0},\qquad a_{n}\neq 0

  • anxna_{n}x^{n} is the leading term; ana_{n} is the leading coefficient
  • the degree is nn, the exponent of the power in the leading term.
  • the long-run behavior of a polynomial is the same as its leading term's behavior.

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