Graphing Polynomials

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What is a polynomial?

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

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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. They are also known as the roots of the polynomial.

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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 algebraic methods.

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What is the leading coefficient of a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 5x^3 + 2x^2 - 3, the leading coefficient is 5.

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What is the end behavior of a polynomial?

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The end behavior of a polynomial describes how the values of the polynomial behave as x approaches positive or negative infinity. It is determined by the degree and leading coefficient.

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What does it mean for a polynomial to be even?

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A polynomial is even if f(-x) = f(x) for all x in its domain. This means the graph is symmetric with respect to the y-axis.

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What does it mean for a polynomial to be odd?

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A polynomial is odd if f(-x) = -f(x) for all x in its domain. This means the graph is symmetric with respect to the origin.

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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, the polynomial x^2 - 5x + 6 can be factored as (x - 2)(x - 3).

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What is the significance of the constant term in a polynomial?

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The constant term is the value of the polynomial when x = 0. It represents the y-intercept of the graph of the polynomial.