3.6 Long and Synthetic Division of Polynomials

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What is polynomial long division?

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Polynomial long division is a method used to divide a polynomial by another polynomial of the same or lower degree, similar to numerical long division.

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What is synthetic division?

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Synthetic division is a simplified form of polynomial division that is used when dividing by a linear factor of the form (x - c). It is faster and requires less writing than long division.

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What is 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 that division 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 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 the result is zero, then (x - c) is a factor.

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What is the first step in polynomial long division?

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The first step in polynomial long division is to divide the leading term of the dividend by the leading term of the divisor.

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What do you do after finding the first term in polynomial long division?

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After finding the first term, multiply the entire divisor by this term and subtract the result from the original polynomial.

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What is the significance of the degree of a polynomial in division?

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The degree of a polynomial helps determine the number of times you can divide it by another polynomial before reaching a remainder.

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What is the standard form of a polynomial?

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The standard form of a polynomial is written in descending order of the degree of its terms, from the highest degree to the lowest.

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What is the result of dividing a polynomial by a polynomial of a higher degree?

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When dividing a polynomial by a polynomial of a higher degree, the result is zero with the original polynomial as the remainder.