Polynomial Division

Front

What is polynomial division?

Back

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 result of dividing a polynomial by a linear factor?

Back

The result is a polynomial of one degree lower than the original polynomial, plus a remainder that can be expressed as a fraction.

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

Back

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 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).

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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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What is the quotient in polynomial division?

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The quotient is the result of the division process, representing how many times the divisor can fit into the dividend.

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What does it mean if the remainder is zero in polynomial division?

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

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How do you perform long division with polynomials?

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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 the process with the new polynomial.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial expression.

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What is a linear polynomial?

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A linear polynomial is a polynomial of degree one, which can be expressed in the form f(x) = ax + b, where a and b are constants.