Graphing Polynomial

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers and coefficients. For example, f(x) = 5x^4 + 2x^3 + 2x - 7 is a 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. For example, in f(x) = 5x^4 + 2x^3 + 2x - 7, the degree is 4.

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What does it mean for a polynomial to have 'n' solutions?

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A polynomial of degree 'n' can have at most 'n' solutions (or roots), which may be real or complex.

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What is the factored form of a polynomial?

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The factored form of a polynomial expresses it as a product of its factors. For example, f(x) = (x-5)^2(x-2)(x+3) is a factored form.

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What is a zero of a polynomial?

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A zero of a polynomial is a value of x that makes the polynomial equal to zero. For example, if f(x) = 0, then x is a zero.

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What is multiplicity in relation to zeros?

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Multiplicity refers to the number of times a particular zero appears in a polynomial. For example, in (x-5)^2, the zero x=5 has a multiplicity of 2.

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What is end behavior of a polynomial function?

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End behavior describes how the values of a polynomial function behave as x approaches positive or negative infinity.

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How do you determine the end behavior of a polynomial?

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The end behavior can be determined by the leading term of the polynomial. For example, if the leading term is positive and of even degree, both ends of the graph will rise.

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What is the significance of the leading coefficient?

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The leading coefficient is the coefficient of the term with the highest degree. It affects the direction of the graph's end behavior.

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What is the relationship between the degree of a polynomial and the number of turns in its graph?

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A polynomial of degree 'n' can have at most 'n-1' turns in its graph.