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{{ printedBook.courseTrack.name }} {{ printedBook.name }} When solving an equation with the Zero Product Property, the first step is factoring the polynomial. Then, each factor is set equal to $0$ and solved as its own equation. $\begin{gathered}
x^3-5x^2+7x-3=0\\
\Downarrow \\
(x-3)(x-1)(x-1)=0\\
\Downarrow \\
x-3=0\\
x-1=0\\
x-1=0
\end{gathered}$
In this case, even though there are three factors, solving them will result in only two unique zeros: $x=3$ and $x=1.$ This occurrence is described as the **multiplicity of zeros**; in the example equation above, the zero $x=3$ has multiplicity $1$ because it only occurs once. On the other hand, $x=1$ has multiplicity $2$ because there are two $(x-1)$ factors.

Note: The multiplicity of a zero being greater than $1$ implies that, algebraically, the zero occurs multiple times. The graph, however, does not intercept the $x\text{-}$axis at this point multiple times. In this example, the zero $x=1$ has a multiplicity of $2$ but the graph intercepts the $x\text{-}$axis at $x=1$ only once.