Polynomial Characteristics Check

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

How do you determine the number of extrema in a polynomial function?

Back

The number of extrema (maximums and minimums) of a polynomial function can be determined by finding the critical points, which are found by taking the derivative and setting it to zero.

Front

What is a relative maximum?

Back

A relative maximum is a point on the graph of a function where the function value is higher than the values of the function at nearby points.

Front

What is a leading coefficient?

Back

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

Front

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

Back

If the leading coefficient is positive, the polynomial will rise to the right; if negative, it will fall to the right.

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial determines the number of possible roots and the general shape of the graph.

Front

What is the difference between even and odd degree polynomials?

Back

Even degree polynomials have symmetrical end behavior (both ends go in the same direction), while odd degree polynomials have opposite end behavior (one end goes up, the other goes down).

Front

What does it mean if a polynomial has a positive leading coefficient?

Back

A polynomial with a positive leading coefficient will have its ends rising as x approaches positive and negative infinity.

Front

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

Back

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