To solve all sorts of problems. Any equation can be written in the form:
(some expression) = 0
Simply by putting everything to the left. It turns out that polynomials are especially easy to solve if you put them in that form - because then you can solve them simply by factoring them. In other cases, for other functions, it might be more of a convention to put them in that form.
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false!
no a plynomial can not have more zeros than the highest (degree) number of the function at leas that is what i was taught. double check the math.
For an algebraic function in one variable, as many as the highest power of the variable.
Assuming it is a function of "x", those are two different names for the same thing.
For a parabola in a normal position ... with its nose either straight up or straight down ... the x-value of the vertex is midway between the zeros of the function, i.e. their average.