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 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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The first step is to 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 original polynomial.

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What is a remainder in Polynomial Long Division?

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A remainder is what is left over after dividing a polynomial when the divisor does not evenly divide the dividend.

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How can you determine if (x - c) is a factor of a polynomial f(x)?

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If f(c) = 0, then (x - c) is a factor of f(x). This is known as the Factor Theorem.

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What is the Factor Theorem?

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The Factor Theorem states that a polynomial f(x) has a factor (x - c) if and only if f(c) = 0.

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What is synthetic division?

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Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor of the form (x - c).

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What is the relationship between Polynomial Long Division and Synthetic Division?

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Both methods are used to divide polynomials, but synthetic division is generally faster and easier when dividing by linear factors.

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What is the result of dividing 2x^3 + 5x^2 + 9 by x + 3?

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

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What does it mean if the remainder is zero in Polynomial Long Division?

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If the remainder is zero, it means that the divisor is a factor of the dividend.