Question 1100353: Suppose f(x) is a polynomial. What is the least possible degree of that polynomial?
x: -24 -18 -12 -6 0 6 12 18 24
f(x): -8 -1 3 -2 4 7 -1 -8 5
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
Every polynomial is a continuous function.
The given value of f(x) show that the function value changes sign 5 times -- between -18 and -12, between -12 and -6, between -6 and 0, between 6 and 12, and between 18 and 24.
Since the function is continuous and the function value changes sign 5 times, the function must have (at least) 5 zeros.
Therefore the minimum degree of the polynomial is 5.
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