The least polynomial of grade 3 represents the graph shown in the figure.
How to determine the least polynomial associated with a graph
In this problem we find the case of a graph, whose least polynomial must be derived. We can infer the least polynomial according to the following symmetry criteria:
- If f(x - a) = f(x + a), where x is the axis of symmetry, then the least polynomial is grade 2.
- If f(x - a) = - f(x + a), where x is the axis of symmetry, then the least polynomial is grade 3.
Then, by direct inspection, we notice that graph fulfills criterion 2, then, we conclude that least polynomial is grade 3.