To determine whether the factor \( (2x + 1) \) has an even or odd multiplicity based on the graph of the polynomial \( w(x) \), you can look for the behavior of the graph at the x-intercept corresponding to \( x = -\frac{1}{2} \) (which is where \( 2x + 1 = 0 \)).
- If the graph crosses the x-axis at that point, the multiplicity of the factor is odd.
- If the graph touches the x-axis and turns around at that point (without crossing), the multiplicity is even.
Since I cannot see the graph, I recommend checking the behavior of the graph at \( x = -\frac{1}{2} \) to determine the multiplicity. Based on that observation, choose either:
- Option #1: even (if it touches and turns around).
- Option #2: odd (if it crosses the x-axis).
Make your decision based on what you observe in the graph.