Polynomial functions

Lessons

• Introduction
  Introduction to Polynomial Functions
  $\cdot$ What is a polynomial function?
  $\cdot$ Exercise:
  State the degree, leading coefficient and constant term for the following polynomial functions:
  1) $f(x) = 9x^{5}+7x^{4}-2x^{3}-12x^{2}+x-10$
  2) $p(x) = -23x^{18}+37x^{15}-11x^{58}+6$

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• 1.
  Recognizing a Polynomial Function

  Which of the following are not polynomial functions? Explain.

  a)

  $f(x) = 5x^{2}+4x-3x^{-1}+2$
  
  
  b)

  $f(x) = -x^{3}+6x^{\frac{1}{2}}$
  
  
  c)

  $f(x) = (\sqrt x + 3)(\sqrt x - 3)$
  
  
  d)

  $f(x) = x^{5}+\pi x-\sqrt7 x^{2}+\frac{3}{11}$
  
  

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• 2.
  Classifying Polynomial Functions by Degree

  Complete the chart:

  

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• 3.
  Classifying Polynomial Functions by Number of Terms
  Write a polynomial satisfying the given conditions:
  i) monomial and cubic
  ii) binomial and linear
  iii) trinomial and quartic

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