Graphing Polynomials in Factored Form Practice

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its factors, which can include linear factors and constants.

Front

What does it mean for a polynomial to be ODD?

Back

A polynomial is considered ODD if f(-x) = -f(x) for all x, meaning its graph is symmetric about the origin.

Front

What does it mean for a polynomial to be EVEN?

Back

A polynomial is considered EVEN if f(-x) = f(x) for all x, meaning its graph is symmetric about the y-axis.

Front

What is multiplicity in the context of polynomial roots?

Back

Multiplicity refers to the number of times a particular root appears in the factored form of a polynomial. A root with an even multiplicity will touch the x-axis, while a root with an odd multiplicity will cross it.

Front

How do you find the real zeros of a polynomial?

Back

To find the real zeros of a polynomial, set the polynomial equal to zero and solve for x.

Front

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

Back

The leading coefficient determines the end behavior of the polynomial's graph. If it's positive, the graph rises to the right; if negative, it falls to the right.

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 can you determine the number of real zeros a polynomial has?

Back

The number of real zeros can be determined by the degree of the polynomial and the nature of its factors, as well as using the Fundamental Theorem of Algebra.

Front

What is the relationship between the degree of a polynomial and its number of turning points?

Back

A polynomial of degree n can have at most n-1 turning points.

Front

What is the factored form of the polynomial f(x) = 2x^3 - 10x^2 + 12x?

Back

The factored form is f(x) = 2x(x - 2)(x - 3).