Polynomials Review

Front

What is a polynomial?

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What is the degree of a polynomial?

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What does the end behavior of a polynomial describe?

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The end behavior of a polynomial describes how the values of the polynomial behave as the input approaches positive or negative infinity. It is determined by the leading term of the polynomial.

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How do you find the maximum value of a polynomial function?

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To find the maximum value of a polynomial function, you can use calculus to find the critical points by setting the derivative equal to zero and then evaluate the function at those points.

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What are real roots of a polynomial?

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What are complex roots of a polynomial?

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Complex roots of a polynomial are roots that include imaginary numbers. They occur in conjugate pairs if the coefficients of the polynomial are real.

Front

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. This implies that a polynomial of degree n has exactly n roots, counting multiplicities.

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What is the relationship between the degree of a polynomial and the number of roots?

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The degree of a polynomial indicates the maximum number of roots it can have. For example, a polynomial of degree 3 can have up to 3 roots.

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What is a leading coefficient?

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What is the difference between real roots and complex roots?

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Real roots are the solutions to the polynomial that are real numbers, while complex roots include imaginary numbers. A polynomial can have both types of roots.