Polynomial Long Division

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What is Polynomial Long Division?

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A method for dividing 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 adding zero terms in Polynomial Long Division?

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To ensure that all degrees of the polynomial are represented, making the division process clearer.

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How do you find the remainder in Polynomial Long Division?

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After the division process is complete, the remainder is what is left over when the degree of the remaining polynomial is less than the degree of the divisor.

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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 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 shape of the polynomial.

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How do you check your work after performing Polynomial Long Division?

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Multiply the quotient by the divisor and add the remainder; the result should equal the original polynomial.

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What is synthetic division?

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A simplified form of polynomial division that can be used when dividing by a linear factor.

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When can you use synthetic division instead of Polynomial Long Division?

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When dividing by a linear polynomial of the form (x - c).