You have probably learned that a zero of a function f(x) is any value c such that f(c)=0. When the function is graphed, the real zeros of the function are the x-intercepts of the graph.

If is a polynomial function, then

c is a zero of the polynomial function f(x),

x-c is a factor of the polynomial function f(x), and

c is a root or solution of the polynomial equation f(x)=0.

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He who knows not and knows not that he knows not is a fool, shun him. He who knows not and knows that he knows not is a child, teach him. He who knows and knows not that he knows is asleep, wake him. And he who knows and knows that he knows is wise, follow him.
-- Persian Proverb