Practice 6-1 
Polynomial
Functions
Find a cubic model for each function. Then use your model
to estimate the
value of y when x = 7.
Write each polynomial in standard form. Then classify it
by degree and by
number of terms .
24. The lengths of the sides of a triangle are x + 4
units, x units, and
x + 1 units. Express the perimeter of the triangle as a polynomial in
standard form.
25. Find a cubic function to model the data below (Hint: Use the number
of years past 1940 for x) Then use the function to estimate the average
monthly Social Security Benefit for a retired worker in 2005.
Average Monthly Social Security Benefits, I940-1999
| Year |
 |
Amount
(in dollars |
 |
25, Find a cubic function to model the data below. (Hint:
Use x to represent
the gestation period.) Then use the function to estimate the longevity of
an animal with a gestation period of 151 days.
Gestation and Longevity of Certain Animals
| Animal |
Rat |
Squirrel |
Pig |
Cow |
Elephant |
Gestation
(in days) |
 |
Longevity
{in years |
 |
Practice 6 -2
Polynomials and Linear
Factors
For each function, determine the zeros, State the
multiplicity of any
multiple zeros.
Write each function in standard form.
9. A rectangular box is 24 in. long,12 in. wide, and 18
in. high. If each
dimension is increased by x in., write a polynomial function in standard
form modeling the volume V of the box,
Write a polynomial function in standard form with
the given zeros
13. -2 multiplicity 3
Write each expression as a polynomial in standard form
Write each function in factored form . Check by
multiplication.
Find the zeros of each function. Then graph the
function .
Find the relative maximum, relative minimum, and zeros
of each function.
Write each polynomial in factored form. Check by
multiplication.
28. A rectangular box has a square base . The combined
length of a side of
the square base, and the height is 20 in. Let x be the length of a side of
the base of the box.
a. Write a polynomial function in factored form modeling the volume
V of the box.
b, What is the maximum possible volume of the box?
Practice 6-3
Dividing Polynomials
Determine whether each binomial is a factor of
.
Divide using synthetic division .
Use synthetic division and the Remainder Theorem to
find P(a).
Divide using long division. Check your answers
Use synthetic division and the given factor to
completely factor each
polynomial function.
Divide.
31. A box is to be mailed. The volume in cubic inches of
the box
can be expressed as the product of its three dimensions:
. The length is x - 8. Find linear
expressions for the other dimensions Assume that the width is
greater than the height.
Reteaching 6 - 4
Solving Polynomial
Equations
OBJECTIVE: Solving polynomial equation by
 MATERIALS: None
factoring |
Example
Solve 
by factoring.
Find all complex roots .
Exercises
Solve each equation by factoring. Find all complex roots.
Practice 6 -4
Solving Polynomial
Equations
Factor the expression on the left side of each
equation. Then solve
the equation.
17. Over 3 yr, Lucia saved$ 550,$ 600,and $650 from
baby-sitting jobs. The
polynomial 
represents her savings, with
interest,
after 3 yr. The annual interest rate equals x -1. Find the interest
needed so that she will have $2000 after 3 yr.
Solve each equation by graphing. Where necessary, round to
the
nearest hundredth.
24, The product of three consecutive integers n - 1,n,and
n +1 is -336.
Write and solve an equation to find the numbers.
Factor each expression
Solve each equation.
.
