# Multiplicities of polynomials

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##### Examples

###### Lessons

- 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:
$P\left( x \right) = - \frac{1}{{12907776}}\left( {x + 3} \right){\left( {x + 1} \right)^2}{\left( {x - 2} \right)^3}{\left( {x - 4} \right)^4}{\left( {x - 7} \right)^5}$