Polynomial Long Division & Remainder Theorem

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What is Polynomial Long Division?

Back

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 Remainder Theorem?

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If a polynomial f(x) is divided by (x - c), the remainder is f(c).

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How do you find the remainder when dividing a polynomial by (x - c)?

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Evaluate the polynomial at c, i.e., find f(c).

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What does it mean for (x - c) to be a factor of a polynomial?

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(x - c) is a factor of f(x) if f(c) = 0.

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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 is the purpose of subtracting in Polynomial Long Division?

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To eliminate the leading term of the current polynomial and simplify the division process.

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What do you do after subtracting in Polynomial Long Division?

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Bring down the next term from the dividend and repeat the division process.

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What is a zero of a polynomial?

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A value of x for which the polynomial evaluates to zero.

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How can you find all zeros of a polynomial?

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Use synthetic division, factoring, or the Rational Root Theorem.

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What is synthetic division?

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A simplified form of polynomial division that uses coefficients to divide a polynomial by a linear factor.