Polynomial Functions, algebra homework help

1. OPEN ENDED Write a quotient of two polynomials such that the remainder is 5.
2. OPEN ENDED Sketch a graph of a function that has one relative maximum point and two relative minimum points.
3. Writing in Math Use the information on page 332 to explain why scientific notation is useful in economics. Include the 2004 national debt of $7,379,100,000,000 and the U.S. population of 293,700,000, both written in words and in scientific notation, and an explanation of how to find the amount of debt per person with the result written in scientific notation and in standard notation.
4. Writing in Math Use the information about tuition increases on page 340 to explain how polynomials can be applied to financial situations. Include an explanation of how a polynomial can be applied to a situation with a fixed percent rate of increase and an explanation of how to use an expression and the 6% rate of increase to estimate Shenequa’s tuition in the fourth year.

Properties of Exponents
GET READY for the Lesson
U.S.
Public Debt
Economists often deal with very
large numbers. For example, the
table shows the U.S. public debt
for several years. Such numbers,
written in standard notation, are
difficult to work with because
they contain so many digits.
Scientific notation uses powers
of ten to make very large or
very small numbers more
manageable.
200,000,000)
LOOD’000’00L *197
Debt ($)
|(16,700,000,000
ODP’000 ‘DOLGLE”
1.233,300,000,000
1900 1930
1990
1960
Year
Source: Bureau of the Public Debe
Multiply and Divide Monomials To simplify an expression containing
powers means to rewrite the expression without parentheses or negative
exponents. Negative exponents are a way of expressing the multiplicative
inverse of a number. For example, can be written as r2. Note that an
expression such as r2 is not a monomial. Why?
KEY CONCEPT
Negative Exponents
Words For any real number a # 0 and any integer n, a
and
Examples 2-3 = and = b
on.
an
EXAMPLE Simplify Expressions with Multiplication
1 Simplify each expression. Assume that no variable equals 0.
a. (3x’y?)(-4x²y4)
(3x*y)(-4x2y4)
= (3.x.x.x.yy).(-4.x.x.yy.yy) Definition of exponents
Commutative Property
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Operations with Polynomials
College Choices
College Tuition
nials
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Shenequa has narrowed her choice for
which college to attend. She is most
interested in Coastal Carolina University,
where the current year’s tuition is $3430.
Shenequa assumes that tuition will
increase at a rate of 6% per year.
You can use polynomials to represent the
increasing tuition costs.
A Magherty College $26,650
ary
omial
$7821
University of
Maryland
03430
Constal Carolina
University
Add and Subtract Polynomials If r represents the rate of increase of
tuition, then the tuition for the second year will be 3430(1 + r). For the
third year, it will be 3430(1 + r)?, or 3430r2 + 6860r + 3430 in expanded
form. The degree of a polynomial is the degree of the monomial with the
greatest degree. For example, the degree of this polynomial is 2.
Tip
EXAMPLE Degree of a Polynomial
O Determine whether each expression is a polynomial. If it is a
polynomial, state the degree of the polynomial.
a. 6x3y5 – 974
This expression is a polynomial because each term is a monomial.
The degree of the first term is 3 + 5 or 8, and the degree of the second
term is 4. The degree of the polynomial is 8.
b. x + x + 5
This expression is not a polynomial because Vă is not a monomial.
cx2 + 3x 1 – 4
This expression is not a polynomial because r-2 and r-1 are not
monomials
. 2-2 = 1 and r-1 = . Monomials cannot contain
variables in the denominator.
CHECK Your Progress
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