Answer:
Odd.
Explanation:
To determine the multiplicity of (2x + 1) as a factor of w(x) based on the given graph, we need to examine the behavior of the graph near the x-intercept (-1/2).
If (2x + 1) is a factor of w(x) with an even multiplicity, it means that the graph of w(x) touches or crosses the x-axis at (-1/2) and has a smooth, even curve at that point.
If (2x + 1) is a factor of w(x) with an odd multiplicity, it means that the graph of w(x) crosses the x-axis at (-1/2) and changes direction, resulting in a sharp "V" or "U" shape at that point.
By observing the given graph, we can see that w(x) intersects the x-axis at (-1/2) and forms a sharp "V" shape. This indicates that (2x + 1) is a factor of w(x) with an odd multiplicity.
In summary, the multiplicity of (2x + 1) as a factor of w(x) is odd based on the graph.