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