Multiplicities of polynomials

Lessons

• 1.
  Sketch the graph of the polynomial function.
  i)

  $P\left( x \right) = x - 2$
  ii)

  $P\left( x \right) = {\left( {x - 2} \right)^2}$
  iii)

  $P\left( x \right) = {\left( {x - 2} \right)^3}$
  iv)

  $P\left( x \right) = {\left( {x - 2} \right)^4}$
  v)

  $P\left( x \right) = {\left( {x - 2} \right)^5}$
  

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• 2.
  Given that the graph shows a degree-eight polynomial and the zero $x = 3$ has a multiplicity of 2, determine the multiplicity of the zero $x = - 2$.
  
  

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• 3.
  Without using a graphing calculator, make a rough sketch of the following polynomial: $P\left( x \right) = - \frac{1}{{12907776}}\left( {x + 3} \right){\left( {x + 1} \right)^2}{\left( {x - 2} \right)^3}{\left( {x - 4} \right)^4}{\left( {x - 7} \right)^5}$

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