Polynomial Key Features

Front

What are the zeros of a polynomial function?

Back

The zeros of a polynomial function are the values of x for which the function equals zero. They are the x-intercepts of the graph.

Tags

CCSS.HSF-IF.C.7C

Front

How can you determine the degree of a polynomial?

Back

The degree of a polynomial is determined by the highest power of the variable in the polynomial expression.

Front

What does it mean if a polynomial has an odd degree?

Back

If a polynomial has an odd degree, its graph will have opposite end behaviors; as x approaches positive infinity, f(x) approaches positive infinity, and as x approaches negative infinity, f(x) approaches negative infinity.

Front

What does it mean if a polynomial has an even degree?

Back

If a polynomial has an even degree, its graph will have the same end behaviors; as x approaches both positive and negative infinity, f(x) approaches either positive or negative infinity.

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 graph of a polynomial?

Back

The sign of the leading coefficient determines the direction of the graph's ends: positive leading coefficients lead to upward ends, while negative leading coefficients lead to downward ends.

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its linear factors.

Front

How do you find the factored form of a polynomial given its zeros?

Back

To find the factored form, use the zeros to create factors of the form (x - zero). For example, if the zeros are 2 and -3, the factored form is (x - 2)(x + 3).

Tags

CCSS.HSF-IF.C.7C

Front

What is the significance of the multiplicity of a zero?

Back

The multiplicity of a zero indicates how many times that zero is repeated in the polynomial. It affects the shape of the graph at that x-intercept.

Tags

CCSS.HSF-IF.C.7C

Front

What is the relationship between the degree of a polynomial and the number of zeros?

Back

A polynomial of degree n can have up to n real zeros, counting multiplicities.