Polynomials and Rationals

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What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

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What is the degree of a polynomial?

Back

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

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What is the leading coefficient of a polynomial?

Back

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

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What is the end behavior of a polynomial?

Back

The end behavior of a polynomial describes how the values of the polynomial behave as the input approaches positive or negative infinity.

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What is a rational function?

Back

A rational function is a function that can be expressed as the ratio of two polynomials.

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What is an asymptote?

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An asymptote is a line that a curve approaches as it heads towards infinity.

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What are vertical asymptotes?

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Vertical asymptotes are vertical lines that correspond to values of x where a rational function approaches infinity.

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What are horizontal asymptotes?

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Horizontal asymptotes are horizontal lines that represent the behavior of a function as x approaches positive or negative infinity.

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How do you find the remainder of a polynomial division?

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You can find the remainder of a polynomial division using the Remainder Theorem, which states that the remainder of the division of a polynomial f(x) by (x - c) is f(c).

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What is synthetic division?

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Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form (x - c).