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What is synthetic division?

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Synthetic division is a simplified form of polynomial long division that is used specifically for dividing a polynomial by a linear factor of the form (x - c). It provides a quick way to find the quotient and remainder.

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State the Remainder Theorem.

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

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What is the Factor Theorem?

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

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How do you find the remainder using synthetic division?

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To find the remainder using synthetic division, set up the synthetic division with the coefficients of the polynomial and the value of c (from x - c). Perform the synthetic division process, and the last number obtained is the remainder.

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What is the first step in synthetic division?

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The first step in synthetic division is to write down the coefficients of the polynomial in descending order of the degree.

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

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

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What does it mean if a polynomial has a factor of (x + 4)?

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If a polynomial has a factor of (x + 4), it means that when the polynomial is evaluated at x = -4, the result is zero (i.e., P(-4) = 0).

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What is the purpose of polynomial long division?

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Polynomial long division is used to divide a polynomial by another polynomial, allowing us to find the quotient and remainder.

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