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

(2x + 1) is a factor of w(x) , whose graph is shown. The multiplicity of (2x + 1) is-example-1
User Knubo
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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.

User Redsquare
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