Polynomial Long Division

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What is Polynomial Long Division?

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A method for dividing a polynomial by another polynomial of the same or lower degree, similar to long division with numbers.

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What is the first step in Polynomial Long Division?

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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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Multiply the entire divisor by the term found and subtract the result from the dividend.

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What is the purpose of finding the remainder in Polynomial Long Division?

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To determine what is left over after the division process, which can be used to check the accuracy of the division.

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How do you determine if a polynomial division is correct?

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Multiply the quotient by the divisor and add the remainder; the result should equal the original dividend.

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What is the remainder theorem?

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If a polynomial f(x) is divided by (x - c), the remainder is f(c).

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

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The degree of the polynomial helps determine the number of times the divisor can fit into the dividend.

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What is a common mistake in Polynomial Long Division?

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Forgetting to subtract the entire product of the divisor and the term found from the dividend.

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How can you check your work in Polynomial Long Division?

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By using synthetic division or substituting values into the original polynomial.

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What is synthetic division?

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A simplified form of polynomial division that is used when dividing by a linear factor.