Answer:
Part A
The degree of f(x) is 7
Part B
The leading coefficient negative
Part C
There are 5 distinct real zeros and 2 relative minimum values
Explanation:
From the of a polynomial from a graph of the polynomial, starting from the left, we have;
1) The graph touches the x-axis (horizontally) and then crosses, which gives a multiplicity of 3
2) The graph crosses the x-axis once going upwards with a multiplicity of 1
3) Next, the graph crosses the x-axis once going downwards with a multiplicity of 1
4) Next, the graph crosses the x-axis once going upwards with a multiplicity of 1
5) Finally, the graph crosses the x-axis once going downwards with a multiplicity of 1
Part A
The degree of f(x) is therefore, 3 + 1 + 1 + 1 + 1 = 7
Part B
The leading coefficient of a polynomial that has an odd degree power with a graph falls to the right and rises to the left, the leading coefficient is negative;
Part C
The number of zeros = 7 zeros
The number of identical zeros = 3 identical zeros
∴ The number of distinct zeros are 7 zeros - 2 identical zeros = 5 distinct zeros
The graph continues from +∞ to -∞, therefore, the number relative minimum value of the polynomial are the two minimum values
The number of relative minimum values = 2
Therefore, there are 5 real distinct zeros and 2 relative minimum values