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What is the Factor Theorem?

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The Factor Theorem states that a polynomial f(x) has a factor (x - c) if and only if f(c) = 0.

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What is the Remainder Theorem?

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The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder of this division is f(c).

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How do you determine if (x - c) is a factor of f(x)?

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To determine if (x - c) is a factor of f(x), evaluate f(c). If f(c) = 0, then (x - c) is a factor.

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What is synthetic division?

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Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form (x - c).

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How do you use synthetic division to evaluate f(c)?

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To evaluate f(c) using synthetic division, set up the synthetic division with c and the coefficients of f(x). The remainder will be f(c).

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What is a zero of a polynomial function?

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A zero of a polynomial function f(x) is a value of x for which f(x) = 0.

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How can you find the real zeros of a polynomial?

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To find the real zeros of a polynomial, factor the polynomial and set each factor equal to zero, then solve for x.

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What does it mean for a polynomial to be factored completely?

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A polynomial is factored completely when it is expressed as a product of irreducible polynomials over the real numbers.

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What is the significance of the degree of a polynomial?

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The degree of a polynomial indicates the highest power of the variable and determines the polynomial's end behavior and the maximum number of real zeros.

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What is the relationship between the factors and the zeros of a polynomial?

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The factors of a polynomial correspond to its zeros; if (x - c) is a factor, then c is a zero of the polynomial.