TEST REVIEW POLYNOMIAL FUNCTIONS

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer.

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. For example, in f(x) = 2x^3 - 4x^2 + 5, the degree is 3.

Front

What does the leading coefficient of a polynomial indicate?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It affects the end behavior of the graph of the polynomial.

Front

How does the leading coefficient affect the end behavior of a polynomial function?

Back

If the leading coefficient is positive, the graph rises to the right; if negative, it falls to the right. The end behavior also depends on whether the degree is odd or even.

Front

What is the end behavior of a polynomial function with an even degree and a positive leading coefficient?

Back

As x approaches -∞, f(x) approaches +∞; as x approaches +∞, f(x) approaches +∞.

Front

What is the end behavior of a polynomial function with an odd degree and a negative leading coefficient?

Back

As x approaches -∞, f(x) approaches +∞; as x approaches +∞, f(x) approaches -∞.

Front

What is the result of multiplying (x^2 - 2x + 1)(x + 1)?

Back

x^3 - x^2 - x + 1.

Front

What is a negative leading coefficient?

Back

A negative leading coefficient means that the term with the highest degree in the polynomial has a negative value, affecting the direction of the graph's end behavior.

Front

What is the difference between even and odd degree polynomials?

Back

Even degree polynomials have symmetrical end behavior, while odd degree polynomials have opposite end behavior.

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial determines the maximum number of roots (x-intercepts) and the general shape of the graph.