Zeros of polynomials

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What are the zeros of a polynomial?

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

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What is the degree of a polynomial?

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Front

What is the Remainder Theorem?

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Front

How do you find the rational zeros of a polynomial?

Back

Front

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

Back

The leading coefficient is the coefficient of the term with the highest degree. It determines the end behavior of the polynomial function.

Front

What is the difference between absolute minimum and relative minimum?

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An absolute minimum is the lowest point over the entire domain of the function, while a relative minimum is the lowest point within a specific interval.

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What does it mean for a polynomial to be factored completely?

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A polynomial is factored completely when it is expressed as a product of its irreducible factors, meaning it cannot be factored further over the set of real numbers.

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What is synthetic division?

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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 thus, a polynomial of degree n has exactly n roots (counting multiplicities).

Front

How do you determine the number of real zeros of a polynomial?

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The number of real zeros can be determined using Descartes' Rule of Signs, which counts the number of sign changes in the polynomial's coefficients.