# Lesson 6Puzzling Over PolynomialsPractice Understanding

Divide out all of the common factors. (Assume no denominator equals .)

### 9.

Why is it important that the instructions say to assume that no denominator equals ?

## Set

Some information has been given for each polynomial. Complete the missing information.

### 10.

Function:

Function in factored form:

End behavior:

As , .

As , .

Roots (with multiplicity):

Degree:

Graph:

### 11.

Function in standard form:

Function in factored form:

End behavior:

As , .

As , .

Roots (with multiplicity):

Degree:

Graph:

### 12.

Function in standard form:

Function in factored form:

End behavior:

As , .

As , .

Roots (with multiplicity):

Degree:

Value of :

Graph:

### 13.

Graph:

Function in standard form:

Function in factored form:

End behavior:

As , .

As , .

Roots (with multiplicity):

Degree:

-intercept:

### 14.

Graph:

Function in standard form:

Function in factored form:

End behavior:

As , .

As , .

Roots (with multiplicity):

Degree:

### 15.

Function in standard form:

Function in factored form:

End behavior:

As , .

As , .

Roots (with multiplicity):

Degree:

-intercept:

Graph:

### 16.

Finish the graph if it is an even function.

### 17.

Finish the graph if it is an odd function.

## Go

Write the polynomial function in standard form given the leading coefficient and the roots of the function.

• Roots: , ,

• Roots: , ,

### 20.

• Roots: ,

Fill in the blanks to make a true statement.

### 21.

If , then a factor of must be .

### 22.

The rate of change in a linear function is always a .

### 23.

The rate of change of a quadratic function is .

### 24.

The rate of change of a cubic function is .

### 25.

The rate of change of a polynomial function of degree can be described by a function of degree .