Zeros of Polynomial Functions

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What are the zeros of a polynomial function?

Back

The zeros of a polynomial function are the values of x for which the function equals zero. They are also known as the roots of the polynomial.

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How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the function 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?

Back

The degree of a polynomial function indicates the maximum number of zeros it can have. For example, a quadratic (degree 2) can have up to 2 zeros.

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What is a real zero?

Back

A real zero is a zero of a polynomial function that is a real number, as opposed to a complex number.

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What is a multiplicity of a zero?

Back

The multiplicity of a zero refers to the number of times a particular zero is repeated in the polynomial. For example, if (x - 2)² is a factor, then 2 is a zero with multiplicity 2.

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What does it mean if a polynomial has an even multiplicity at a zero?

Back

If a polynomial has an even multiplicity at a zero, the graph touches the x-axis at that zero but does not cross it.

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What does it mean if a polynomial has an odd multiplicity at a zero?

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If a polynomial has an odd multiplicity at a zero, the graph crosses the x-axis at that zero.

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What is the Factor Theorem?

Back

The Factor Theorem states that if f(c) = 0 for a polynomial f(x), then (x - c) is a factor of f(x).

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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).

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How can you verify if a number is a zero of a polynomial?

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To verify if a number c is a zero of a polynomial f(x), substitute c into the polynomial. If f(c) = 0, then c is a zero.