Question

(2x+1)
is a factor of w(x), whose graph is shown. Is the multiplicity of (2x+1)
even or odd?

Option #1: even

Option #2: odd

(1 point)

Answer 1

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.