Pre-Calculus HWK Section 2.4 Zeros of Polynomial Functions

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What is a zero of a polynomial function?

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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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How do you find the zeros of a polynomial function?

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To find the zeros of a polynomial function, you can use methods such as factoring, the Rational Root Theorem, synthetic division, or numerical methods.

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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 has at least one complex root, and the total number of roots (including multiplicities) is equal to the degree of the polynomial.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial expression.

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What is synthetic division?

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Synthetic division is a simplified form of polynomial long division that is used to divide a polynomial by a linear factor.

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What is the Rational Root Theorem?

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The Rational Root Theorem provides a way to find all possible rational roots of a polynomial equation by considering the factors of the constant term and the leading coefficient.

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How can you determine the number of real zeros of a polynomial function?

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You can determine the number of real zeros using Descartes' Rule of Signs, which analyzes the number of sign changes in the polynomial's coefficients.

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What is Descartes' Rule of Signs?

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Descartes' Rule of Signs states that the number of positive real zeros of a polynomial is equal to the number of sign changes between consecutive non-zero coefficients, or less than that by an even number.

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What is a complex zero?

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

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The zeros of a polynomial correspond to the values of x that make the polynomial equal to zero, and each zero can be expressed as a factor of the polynomial in the form (x - zero).