(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)

1 answer

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.