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

Question

Option #1: even

Option #2: odd

Answer 1

The multiplicity of (2x+1) can be determined by looking at the behavior of the graph of w(x) around the x-intercept where (2x+1) is equal to 0.

From the graph, we can see that the graph of w(x) crosses the x-axis at the x-intercept of -0.5. Since the graph crosses the x-axis at the x-intercept, the multiplicity of (2x+1) is odd.

Therefore, the correct option is: Option #2: odd.