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) = 2x^3 + 3x^2 - 5 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 expression. For example, in f(x) = 5x^4 + 2x^3 + 2x - 7, the degree is 4.

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How many solutions can a polynomial of degree n have?

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A polynomial of degree n can have at most n solutions (real or complex). For example, a polynomial of degree 4 can have up to 4 solutions.

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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-1)(x-2)(x-3) is a factored form of a cubic polynomial.

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What does it mean for a zero to have multiplicity?

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Multiplicity refers to the number of times a particular zero (or root) appears in the factored form of a polynomial. For example, in (x-2)^3, the zero x=2 has a multiplicity of 3.

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What is the end behavior of a polynomial function?

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The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.

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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 equals zero. For example, the zeros of f(x) = (x+4)(x-3)(x-2) are x = -4, 3, and 2.

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How do you find the zeros of a polynomial?

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To find the zeros of a polynomial, set the polynomial equal to zero and solve for x. This can involve factoring, using the quadratic formula, or other methods.

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

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

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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, where a, b, c, and d are constants and a ≠ 0.