12/3 Key Features of Polynomials

Front

What is a polynomial?

Back

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. It determines the end behavior of the polynomial function.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by its leading term. If the leading coefficient is positive and the degree is even, both ends of the graph will rise. If the leading coefficient is positive and the degree is odd, the left end will fall and the right end will rise.

Front

What is the standard form of a polynomial?

Back

Front

What is the degree of a polynomial?

Back

Front

What is an interval of increase in a polynomial function?

Back

An interval of increase is a range of x-values where the function's output (y-value) is increasing. This can be determined by analyzing the graph or the first derivative of the polynomial.

Front

What is a polynomial function?

Back

Front

Back

Front

What does it mean for a polynomial to be in factored form?

Back

Front

How can you identify the number of real roots of a polynomial?

Back

The number of real roots can be determined by analyzing the graph of the polynomial or using the Fundamental Theorem of Algebra, which states that a polynomial of degree n has exactly n roots, counting multiplicities.