A _______ of a polynomial is a number x such that P(x)=0.

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Multiple Choice

A _______ of a polynomial is a number x such that P(x)=0.

Explanation:
Zeros of a polynomial are the x-values that make P(x) equal to zero. These x-values are called roots. This is why the statement P(a) = 0 identifies a as a root of the polynomial (and, by the Factor Theorem, x − a is a factor of P(x)). The other terms don’t match this idea: a vertex is the turning point of a graph, not a value that makes the polynomial zero; a coefficient is simply a number that scales a term; a derivative describes the rate of change, not where the function hits zero. For example, if P(x) = x^2 − 5x + 6, then P(2) = 0 and P(3) = 0, so x = 2 or x = 3 are the roots.

Zeros of a polynomial are the x-values that make P(x) equal to zero. These x-values are called roots. This is why the statement P(a) = 0 identifies a as a root of the polynomial (and, by the Factor Theorem, x − a is a factor of P(x)). The other terms don’t match this idea: a vertex is the turning point of a graph, not a value that makes the polynomial zero; a coefficient is simply a number that scales a term; a derivative describes the rate of change, not where the function hits zero. For example, if P(x) = x^2 − 5x + 6, then P(2) = 0 and P(3) = 0, so x = 2 or x = 3 are the roots.

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