Polynomial Long and Synthetic Division

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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 first step in Polynomial Long Division?

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The first step is to arrange the dividend and divisor in descending order of their degrees.

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What do you do with the leading term of the divisor in Long Division?

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You divide the leading term of the dividend by the leading term of the divisor to find the first term of the quotient.

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What is the purpose of subtracting in Polynomial Long Division?

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Subtracting helps to eliminate the leading term of the dividend, allowing you to bring down the next term and continue the division process.

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What is a remainder in Polynomial Division?

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A remainder is what is left over after dividing a polynomial. It can be expressed as a polynomial of lower degree than the divisor.

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How do you check your work in Polynomial Long Division?

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You can check your work by multiplying the quotient by the divisor and adding the remainder. The result should equal the original dividend.

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What is the significance of inserting zero coefficients in Polynomial Long Division?

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Inserting zero coefficients ensures that all degrees of the polynomial are represented, which is crucial for accurate division.

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What is the next step after writing down the first term of the quotient in Long Division?

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Multiply the entire divisor by the first term of the quotient and subtract the result from the dividend.