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 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 subtracting in Polynomial Long Division?

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To eliminate the leading term of the dividend and simplify the polynomial for further division.

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What do you do if the degree of the remainder is less than the degree of the divisor?

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You stop the division process; the remainder is the final answer.

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How do you express the final answer in Polynomial Long Division?

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

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What is the quotient in the division of (2x^3 + 5x^2 + 9) by (x + 3)?

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The quotient is 2x^2 - x + 3.

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What is the remainder when dividing (2x^3 + 5x^2 + 9) by (x + 3)?

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The remainder is 0, indicating that (x + 3) is a factor of the polynomial.

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

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The leading coefficient helps determine the first term of the quotient and influences the overall division process.

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What is synthetic division and how does it relate to Polynomial Long Division?

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Synthetic division is a simplified form of polynomial division that can be used when dividing by linear factors.