The Zero Product Property states that if \( a\cdot b = 0 \), then at least one of \( a\) or \( b\) must be equal to zero. We can use this fact to solve many problems, but in particular, it is helpful when dealing with polynomials that we have factored.

If we know that \( (x+1)(x-3) = 0 \), we can conclude that one of the following MUST be true:

\[ \begin{align} x+1 &= 0 \\ x-3 &=0. \end{align} \]

Thus, \(x\) must be one of \( -1, 3\).

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