Question

The x-axis ranges from negative 3 to 4 in increments of 0.5. The y-axis ranges from negative 4 to 20 in increments of 2. The plot starts at approximately left parenthesis negative 1.6 comma negative 4 right parenthesis. It passes through the x-axis at negative 1.5 as it rises steeply to a turning point at left parenthesis negative 0.7 comma 16.5 right parenthesis. It descends to an inflection point on the x-axis at approximately 0.8 and gently rises to an inflection point at left parenthesis 2.1 comma 2 right parenthesis. The curve descends to a turning point on the x-axis at 3 and then rises steeply. The plot terminates just beyond left parenthesis 3.8 comma 20 right parenthesis. All values are approximate.Consider the graph of the polynomial function p(x). Given that (2x+3)is a factor of p(x), which of the following could be the multiplicity of (2x+3)?

Answer 1

Because the graph crosses the x-axis at x = −1.5, the root is of odd multiplicity. It crosses steeply (no flattening/horizontal tangent), so the multiplicity is 1 (a simple root).