5. Characteristics of Polynomials Review 2024

Front

What is a polynomial?

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What is the degree of a polynomial?

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How do you find the roots of a polynomial?

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The roots of a polynomial are the values of the variable that make the polynomial equal to zero. They can be found using factoring, the quadratic formula, or numerical methods.

Front

What is a quadratic polynomial?

Back

Front

What is the difference between even and odd degree polynomials?

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Even degree polynomials have the highest power as an even number and their graphs are symmetric about the y-axis. Odd degree polynomials have the highest power as an odd number and their graphs are symmetric about the origin.

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What are the characteristics of the graph of a polynomial function?

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The graph of a polynomial function is continuous and smooth, with no breaks or sharp corners. The number of turning points is at most one less than the degree of the polynomial.

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What is the leading coefficient of a polynomial?

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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. A polynomial of degree n has exactly n roots, counting multiplicities.

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How do you determine the number of roots of a polynomial?

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The number of roots of a polynomial can be determined by its degree. A polynomial of degree n can have up to n real roots.

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What is synthetic division?

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