Polynomial Long 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 lower degree, similar to numerical long division.

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What is the first step in Polynomial Long Division?

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The first step is to divide the leading term of the dividend by the leading term of the divisor.

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How do you handle the remainder in Polynomial Long Division?

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The remainder is expressed as a fraction with the divisor as the denominator, added to the quotient.

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What is the quotient in the division of (4x^3 + 6x^2 + 8) ÷ (x + 4)?

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The quotient is 4x^2 + 2x + 4.

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What is the result of dividing (3x^3 + 4x^2 + 5) by (x + 2)?

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The result is 3x^2 + 2x + 1.

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What is the quotient when dividing (5x^3 + 7x^2 + 10) by (x + 5)?

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The quotient is 5x^2 + 2x + 5.

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What does it mean if the degree of the dividend is less than the degree of the divisor in Polynomial Long Division?

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If the degree of the dividend is less than the degree of the divisor, the quotient is 0 and the dividend is the remainder.

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What is the quotient of (2x^3 + 5x^2 + 9) ÷ (x + 3)?

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

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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 how to scale the divisor to eliminate the leading term of the dividend.

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What is the process of subtracting in Polynomial Long Division?

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After multiplying the divisor by the current term of the quotient, subtract the result from the dividend to find the new dividend.