Understanding multiplicities of polynomials

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

Multiplicities of polynomials