Polynomial Division

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What is polynomial division?

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Polynomial division is the process of 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 quotient in polynomial division?

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The quotient is the result of the division of one polynomial by another, representing how many times the divisor fits into the dividend.

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What is the remainder in polynomial division?

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The remainder is what is left over after dividing one polynomial by another when the divisor does not evenly divide the dividend.

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How do you perform polynomial long division?

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1. Divide the leading term of the dividend by the leading term of the divisor. 2. Multiply the entire divisor by this result. 3. Subtract this from the dividend. 4. Repeat with the new polynomial until the degree of the remainder is less than the degree of the divisor.

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What is synthetic division?

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Synthetic division is a simplified form of polynomial division that is used when dividing by a linear factor of the form (x - c). It is faster and requires less writing than long division.

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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 the Remainder Theorem?

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The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).

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The remainder is zero.