PC Ch 2 - Zeros of Polynomial Functions

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Define a zero of a polynomial function.

Back

A zero of a polynomial function is a value of x for which the polynomial evaluates to zero, meaning P(x) = 0.

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What is the Fundamental Theorem of Algebra?

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The Fundamental Theorem of Algebra states that every non-constant polynomial function of degree n has exactly n complex roots, counting multiplicities.

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Explain synthetic division.

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor of the form (x - c).

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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 polynomial equal to zero and solve for x using factoring, synthetic division, or the quadratic formula.

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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 indicates the maximum number of zeros it can have, including complex and repeated zeros.

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What is a complex zero?

Back

A complex zero is a solution to a polynomial equation that includes imaginary numbers, typically in the form a + bi, where a and b are real numbers.

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Explain the concept of multiplicity in relation to polynomial zeros.

Back

Multiplicity refers to the number of times a particular zero is repeated in a polynomial. A zero with an even multiplicity will touch the x-axis, while one with an odd multiplicity will cross it.