polynomial functions

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What is a polynomial function?

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A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer.

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What determines the end behavior of a polynomial function?

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The end behavior of a polynomial function is determined by the leading coefficient and 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 a leading coefficient?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

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What is a cubic polynomial?

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A cubic polynomial is a polynomial of degree 3, which can be expressed in the form f(x) = ax^3 + bx^2 + cx + d.

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What is a quadratic polynomial?

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A quadratic polynomial is a polynomial of degree 2, expressed in the form f(x) = ax^2 + bx + c.

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What is a binomial?

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A binomial is a polynomial that contains exactly two terms, such as x + 1 or 3x^2 - 2.

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What is a monomial?

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A monomial is a polynomial that contains exactly one term, such as 5x^3 or -2.

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How do you identify the degree of a polynomial from its graph?

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The degree of a polynomial can often be identified by the number of turning points in its graph. A polynomial of degree n can have at most n-1 turning points.

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What is the end behavior of a polynomial with an even degree and a positive leading coefficient?

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The end behavior of a polynomial with an even degree and a positive leading coefficient rises to positive infinity on both ends.