Flashcard 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 a_n ≠ 0.

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

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. For f(x) = 2x^3 - 3x^2 + 4, the leading coefficient is 2.

Front

What are x-intercepts of a polynomial function?

Back

X-intercepts are the points where the graph of the polynomial crosses the x-axis. They occur where f(x) = 0.

Tags

CCSS.HSF-IF.C.7C

Front

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

Back

To find the x-intercepts, set the polynomial equal to zero and solve for x. For example, for f(x) = x^2 - 4, set x^2 - 4 = 0.

Tags

CCSS.HSF-IF.C.7C

Front

What is the maximum number of x-intercepts a polynomial can have?

Back

A polynomial of degree n can have at most n x-intercepts.

Tags

CCSS.HSF-IF.C.7C

Front

What is the significance of the leading term in a polynomial?

Back

The leading term determines the end behavior of the polynomial function. For example, if the leading term is positive and of even degree, the ends of the graph will rise.

Front

What is the relationship between the degree of a polynomial and the number of turns in its graph?

Back

The maximum number of turns in the graph of a polynomial function is one less than its degree. For a cubic polynomial (degree 3), the maximum number of turns is 2.

Front

How do you use the leading-term test to determine the end behavior of a polynomial?

Back

The leading-term test involves analyzing the leading term's degree and coefficient. If the leading term is positive and of even degree, the graph rises on both ends.

Front

What is synthetic division and when is it used?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor of the form (x - c). It is faster and easier than long division.

Tags

CCSS.HSA.APR.D.6