The graph of a polynomial function has four turning points. What is the least possible degree of this polynomial?

Question

(1 point)
Responses

3
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Answer 1

The number of turning points of a polynomial function is related to its degree. Specifically, a polynomial of degree \( n \) can have at most \( n - 1 \) turning points.

In this case, since the polynomial has four turning points, the least possible degree \( n \) can be determined by the inequality:

\[ n - 1 \geq 4 \]

Solving this gives:

\[ n \geq 5 \]

Therefore, the least possible degree of the polynomial is 5.

So the answer is:

5