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What is polynomial long division?

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Polynomial long division is a method used to divide a polynomial by another polynomial of the same or lower degree, similar to numerical long division.

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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 the result and subtract from the dividend. 3. Repeat the process with the new polynomial until the degree of the remainder is less than the degree of the divisor.

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What is the remainder theorem?

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The remainder theorem states that when a polynomial f(x) is divided by (x - c), the remainder is f(c).

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What is synthetic division?

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Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor of the form (x - c).

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What is the difference between a polynomial and a rational function?

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A polynomial is a mathematical expression consisting of variables raised to whole number powers, while a rational function is a ratio of two polynomials.

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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.

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What is a leading coefficient?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

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What does it mean for a polynomial to be factored?

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Factoring a polynomial means expressing it as a product of its factors, which can be polynomials of lower degrees.

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What is the significance of the x-intercepts of a polynomial?

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The x-intercepts of a polynomial are the values of x for which the polynomial equals zero; they represent the roots of the polynomial.

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What is the relationship between the degree of a polynomial and the number of roots it can have?

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A polynomial of degree n can have at most n roots, counting multiplicities.