Polynomials

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial equals zero.

Front

How do you determine 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 significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the direction of the polynomial's end behavior and affects the shape of the graph.

Front

What does it mean for a zero to have multiplicity?

Back

Multiplicity refers to the number of times a particular zero is repeated in a polynomial.

Front

What effect do odd multiplicities have on the graph of a polynomial at its zeros?

Back

Odd multiplicities cause the graph to cross the x-axis at the zero.

Front

What effect do even multiplicities have on the graph of a polynomial at its zeros?

Back

Even multiplicities cause the graph to bounce off the x-axis at the zero.

Front

How can you express a polynomial given its zeros and their multiplicities?

Back

A polynomial can be expressed as a product of factors corresponding to its zeros, raised to their respective multiplicities.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written as a sum of terms in descending order of the degree.

Front

What is the difference between a polynomial and a non-polynomial function?

Back

A polynomial function consists of terms with non-negative integer exponents, while non-polynomial functions may include negative exponents, fractions, or irrational numbers.

Front

How do you find the x-intercepts of a polynomial function?

Back

The x-intercepts of a polynomial function are found by solving the equation of the polynomial set to zero.