Understanding multiplicities of polynomials

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Sketch the graph of the polynomial function.
i)
$P\left( x \right) = x - 2$ $P (x) = x - 2$
ii)
$P\left( x \right) = {\left( {x - 2} \right)^2}$ $P (x) = (x - 2)^{2}$
iii)
$P\left( x \right) = {\left( {x - 2} \right)^3}$ $P (x) = (x - 2)^{3}$
iv)
$P\left( x \right) = {\left( {x - 2} \right)^4}$ $P (x) = (x - 2)^{4}$
v)
$P\left( x \right) = {\left( {x - 2} \right)^5}$ $P (x) = (x - 2)^{5}$
Given that the graph shows a degree-eight polynomial and the zero $x = 3$ $x = 3$ has a multiplicity of 2, determine the multiplicity of the zero $x = - 2$ $x = - 2$ .
Without using a graphing calculator, make a rough sketch of the following polynomial: $P\left( x \right) = - \frac{1}{{12907776}}\left( {x + 3} \right){\left( {x + 1} \right)^2}{\left( {x - 2} \right)^3}{\left( {x - 4} \right)^4}{\left( {x - 7} \right)^5}$ $P (x) = - \frac{1}{12907776} (x + 3) (x + 1)^{2} (x - 2)^{3} (x - 4)^{4} (x - 7)^{5}$

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