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What is a zero of a polynomial?

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A zero of a polynomial is a value of x that makes the polynomial equal to zero. It is also known as a root of the polynomial.

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How do you find the zeros of a polynomial function?

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To find the zeros of a polynomial function, set the polynomial equal to zero and solve for x. This can involve factoring, using the quadratic formula, or graphing.

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What is the relationship between the degree of a polynomial and the number of zeros?

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The degree of a polynomial indicates the maximum number of zeros it can have. For example, a polynomial of degree 3 can have up to 3 zeros.

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What does it mean for a zero to have multiplicity?

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Multiplicity refers to the number of times a particular zero is repeated. For example, if (x - 2) appears twice in the factorization, then x = 2 has a multiplicity of 2.

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How can you determine the multiplicity of a zero from a polynomial's factors?

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The multiplicity of a zero can be determined by the exponent of its corresponding factor. For example, in the factor (x - 3)^2, the zero x = 3 has a multiplicity of 2.

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What is the factored form of a polynomial?

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What is the significance of the leading coefficient in a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree. It affects the end behavior of the polynomial's graph.

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How do you identify the zeros of a polynomial from its graph?

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The zeros of a polynomial can be identified as the x-intercepts of its graph, where the graph crosses or touches the x-axis.

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What is the relationship between the factors and zeros of a polynomial?

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Each zero of a polynomial corresponds to a factor of the form (x - zero). For example, if x = 3 is a zero, then (x - 3) is a factor.

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What is the Remainder Theorem?

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The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder is f(c). This can help find zeros.