Polynomial Division Review

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What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial of equal or lower degree, resulting in a quotient and a remainder.

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What is synthetic division?

Back

Synthetic division is a simplified form of polynomial division that uses only the coefficients of the polynomial and is typically used when dividing by a linear factor.

Front

When should you use long division instead of synthetic division?

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Long division should be used when dividing by a polynomial of degree greater than 1 or when the divisor is not a linear factor.

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What is the remainder theorem?

Back

The remainder theorem states that when a polynomial f(x) is divided by (x - c), the remainder is 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 set up synthetic division?

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To set up synthetic division, write the coefficients of the polynomial in descending order and place the zero of the divisor (c) to the left.

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What is the significance of using a zero placeholder in synthetic division?

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A zero placeholder is used in synthetic division to maintain the correct degree of the polynomial when a term is missing.

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What is the general form of the result from polynomial division?

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The result of polynomial division is expressed as: Quotient + (Remainder / Divisor).

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What does the leading coefficient of a polynomial indicate?

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The leading coefficient indicates the term with the highest degree and affects the end behavior of the polynomial graph.

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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 expression.