To fill in the missing values in the factored form of \( q(x) = (x+4)(x+ )(x−) \), we need to analyze the graph of the function \( q(x) \).
Typically, the missing values in a factored expression represent the x-intercepts (roots) of the polynomial. If the graph of the function q(x) shows intercepts where it crosses the x-axis, we can use those points to find the missing factors.
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Identify the x-intercepts on the graph: Look at where the graph crosses the x-axis. If there are values \( r_1 \) and \( r_2 \), then these correspond to the factors \( (x + r_1) \) and \( (x - r_2) \).
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Insert the missing values: For example, if you identify that the graph has x-intercepts at -2 and -3, the factored form would look like: \[ q(x) = (x + 4)(x + 2)(x + 3) \]
You could also have a repeated root (a double root) if the graph just touches the x-axis at that point without crossing it.
Please provide a description of the graph, such as the coordinates of the x-intercepts, so I can help specify the missing values accurately.
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