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 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 a remainder in Polynomial Long Division?

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The value left over after dividing a polynomial, which cannot be divided by the divisor anymore.

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

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Use the Remainder Theorem: if f(c) = 0, then (x - c) is a factor.

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What is the Remainder Theorem?

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It states that the remainder of the division of a polynomial f(x) by (x - c) is f(c).

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

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It means that the divisor is a factor of the dividend.

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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 result of the division, 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 helps determine the first term of the quotient and influences the overall division process.