Polynomials Review

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

Front

What is the degree of a polynomial?

Back

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

Front

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.

Front

What does it mean for a polynomial to be even or odd?

Back

A polynomial is even if all its terms have even degrees, and it is odd if all its terms have odd degrees.

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as the input values approach positive or negative infinity.

Front

What is the significance of the degree of a polynomial in determining its end behavior?

Back

The degree of a polynomial determines the direction of the ends of the graph: odd degree polynomials have opposite end behaviors, while even degree polynomials have the same end behavior.

Front

How can you determine the number of x-intercepts of a polynomial?

Back

The number of x-intercepts can be determined by the degree of the polynomial and the nature of its roots (real or complex).

Front

What is a local maximum or minimum in the context of polynomial functions?

Back

A local maximum is a point where the function value is higher than all nearby points, while a local minimum is a point where the function value is lower than all nearby points.

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root.

Front

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

Back

A polynomial is a function that can be expressed as a sum of terms with non-negative integer exponents, while a rational function is a ratio of two polynomials.