Polynomial Long Division

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What is Polynomial Long Division?

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A method used to divide 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 dividing the leading terms in Polynomial Long Division?

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Multiply the entire divisor by the result from the first step and subtract this from the dividend.

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What is the purpose of subtracting in Polynomial Long Division?

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To eliminate the leading term of the dividend and bring down the next term.

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What do you do after subtracting in Polynomial Long Division?

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Repeat the process: divide, multiply, and subtract until the degree of the remainder is less than the degree of the divisor.

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What is a remainder in Polynomial Long Division?

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The leftover polynomial after the division process is complete, which cannot be divided by the divisor.

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How do you express the result of Polynomial Long Division?

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The result is expressed as the quotient plus the remainder divided by the divisor.

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What is the quotient in Polynomial Long Division?

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The polynomial obtained from the division process, representing how many times the divisor fits into the dividend.

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What is the significance of the leading coefficient in Polynomial Long Division?

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It determines the first term of the quotient and affects the overall division process.

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How do you handle polynomials with missing degrees during Polynomial Long Division?

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Insert a placeholder (0) for any missing degrees to maintain the correct structure of the polynomial.