Using Polynomials in the “Real World”
Polynomial functions are used in our everyday lives in a few different ways, this includes art, architecture, construction, financial planning, and manufacturing. We can also calculate how long it will take one person to do a job alone when we know how long it takes a group to get it done as well. Farmers on crop farms work dawn to dusk through the growing season to produce the grains, fruits, and vegetables that feed the country. These equations help them to determine how long they need to work on a certain project.

One application of polynomials is that for any smooth curve we can approximate this curve by a graph of a polynomial function with sufficient degree. If you have real life data up to certain time, you can sketch the graph of the data and you want to predict the behavior of the data in the future. One way to solve this is to approximate the curve that you obtained from your data by a graph of a polynomial function hoping that this polynomial function can also approximate the data in the future. Polynomial equations are also used in creating buildings, landscapes and even roller coasters.

Lastly, and most importantly, using polynomials to pass high school and college. In every math class, using polynomials to graph and to find the possible rational zeroes is a big part in getting an A in the class. If you don’t know how to to this stuff then you can’t keep doing harder and harder math, like going from pre calculus to calculus.

...Saint George
International School
Of Panama
Algebra
Polynomials and PolynomialsFunctions
Laura D. Rosas M.
VII Galileo Galilei
Prof. Ángel F. Torralba
30.10.12
Index
1. Introduction
2. Area of Investigation
3. Problem
4. Bank Collection Data
5. Hypothesis
6. Argumentation
7. Conclusion
8. Recommendation
9. Illustration
10. Bibliography
11. Evaluation Sheet
1. Introduction
In this formal investigation we’re talking about polynomials and its functions in addition, subtraction, multiplication, and division. Polynomials are used in every type of mathematics, mostly in algebra. Polynomials refer to a finite sum of terms in which all variables have a whole number exponents and no variable appears in a denominator.
In this formal we also talk about the diverse ways of adding, subtracting, multiplying, and dividing polynomials. One of the ways for multiplying polynomials includes the FOIL procedure that refers to: First terms, Outer terms, Inner terms, and Last terms. It is one of the most common ways for multiplying polynomials and it is one of the ways that we’re going to use in the multiplication of polynomials.
We’re also going to show diverse polynomialsfunctions graphs that are very used when showing the functions of...

...POLYNOMIALFUNCTIONS ACTIVITY
NCTM Addenda Series/Grades 9-12
The Park and Planning Commission decided to consider three factors when attempting to improve the daily profits at their sports facility:
❖ The number of all-day admission tickets sold
❖ The cost of operating the facility
❖ The price of each all-day admission ticket
After carefully analyzing their operating costs, they found that it would be impossible to cut them further.
Daily Operating Costs
Advertisements $ 55.00
Employees’ pay 310.00
Heat, lights, taxes, food, rent 435.00
Knowing that the maximum number of potential patrons is 200, the Park and Planning Commission decided to vary the price of each admission ticket to see what effect this change might have on the number of tickets sold. After much experimentation, they collected the following sales data:
Ticket Price [in $] Average Number of Tickets Sold
________________________________________________________________________
5. 158
7 142
9. 119
11 97
1. Using this information, suggest the optimal ticket price for all-day admission to the
sports facility. If you feel the need for more information, please explain why.
2. Use a graphing calculator to find the function...

...Lab Report
Title: PolynomialFunctions
Materials used:
* A cylindrical object such as a soup can or thermos
* Ruler or tape measure
* Graphing technology (e.g., graphing calculator or GeoGebra)
Procedure
1. Measure and record the diameter and height of the cylindrical object you have chosen in inches. Round to the nearest whole number.
2. Apply the formula of a right circular cylinder (V = r2h) to find the volume of the object. (Note: Be sure to find the radius from the diameter measurement by dividing by 2.)
Now suppose you knew the volume of this object and the relation of the height to the radius, but did not know the radius. Rewriting the equation with one variable would result in a polynomial equation that you could solve to find the radius.
3. Rewrite the formula using the variable x for the radius. Substitute the value of the volume found in step 2 for V and express the height of the object in terms of x plus or minus a constant. For example, if the height measurement is 4 inches longer than the radius, then the expression for the height will be (x + 4).
4. Simplify the equation and write it in standard form. Multiply each term in the equation by 100 to eliminate any decimals, if necessary.
5. Find the solutions to this equation algebraically using the Fundamental Theorem of Algebra, the Rational Root Theorem, Descartes' Rule of Signs, and the Factor Theorem.
(Hint: If the numbers...

...STUDIESTODAY.COM
Chapter - 2
(Polynomials)
Key Concepts
Constants : A symbol having a fixed numerical value is called a constant.
Example : 7, 3, -2, 3/7, etc. are all constants.
Variables : A symbol which may be assigned different numerical values is known as
variable.
Example :
C - circumference of circle
r - radius of circle
Where 2 &
are constants. while C and r are variable
Algebraic expressions : A combination of constants and variables. Connected by
some or all of the operations +, -, X and
Example :
is known as algebraic expression.
etc.
Terms : The several parts of an algebraic expression separated by '+' or '-' operations
are called the terms of the expression.
Example :
is an algebraic expression containing 5
terms
Polynomials : An algebraic expression in which the variables involved have only nonnegative integral powers is called a polynomial.
(i)
(ii)
is a polynomial in variable x.
is an expression but not a polynomial.
Polynomials are denoted by
Coefficients : In the polynomial
, coefficient of
respectively and we also say that +1 is the constant term in it.
Degree of a polynomial in one variable : In case of a polynomial in one variable the
highest power of the variable is called the degree of the polynomial.
Classification of polynomials on the basis of degree.
14
ISSUED BY KENDRIYA...

...
Financial Polynomials
Ashford University
Abstract
In this paper I will be demonstrating how to use financial polynomials with a few expressions from the textbook “Elementary and Intermediate Algebra”. I will not only show the problem, but also will also break the expression down showing all mathematical work, and provide reasoning of how anybody can apply this theory to everyday life. In the paper there will be the following words: FOIL, like terms, Descending order, Dividend, and Divisor highlighted and explained.
In the text we are given the following expression . With this expression we are to evaluate the polynomial using :
P=$200 and r= 10%, and
P=$5670 and r=3.5%
First we have to rewrite the expression without the parenthesis. One way to do this is to use a process called the FOIL method were we will multiple across the binomial using the steps of the FOIL method.
P(1+r/2)2 The original expression
P(1+r/2)*(1+r/2) Square the quantity (1+r/2)2 this will cancel out the exponent
P(1+r/2+r/2+r2/2) Here is were the FOIL method comes into play when there are Like terms they need to be combined.
P(1+r+r2/4) After FOIL method move (P) across the expression
P+Pr+Pr2/4 After parenthesis are moved here is what our expression looks like. Now we are ready to move to our second step inputting the above numbers into our expression.
P+Pr+Pr2/4 The original expression
(P)200+(P)200*((r )0.1)+(p)200*((r)...

...Lesson 03.01: Review of Polynomials
Types of Expressions
Type
Definition
Example
Monomial
An expression with one term
5x
Binomial
An expression with two terms
g + 3
Trinomial
An expression with three terms
m2 + m + 1
Polynomial
An expression containing four or more terms
a5 – 3a4 – 7a3 + 2a – 1
Polynomial Arrangement
A polynomial in descending order is written with the terms arranged from largest to smallest degree.
Example: s3 – s2 + 3s – 7
A polynomial in ascending order is written with the terms arranged from smallest to largest degree.
Example: –9 + r2 + 4r4
Degree of Polynomials
The degree of a polynomial is equal to the degree of the term with the highest sum of exponents.
Example: z3 + 7z2 – 11z + 24, degree 3
Example: 5r3s – 6rs2 + q – 8, degree 4
Lesson 03.02: Polynomial Operations
Adding Polynomials
Distribute any coefficients
Combine like terms
(4x3 + 5x2 – 2x – 7) + (2x3 – 6x2 – 2)
4x3 + 5x2 – 2x – 7 + 2x3 – 6x2 – 2
6x3 – x2 – 2x – 9
Subtracting Polynomials
Distribute any coefficients – don’t forget to distribute the understood negative one!
Combine like terms
(9x2 – 7) – (8x2 + 2x + 10)
9x2 – 7 – 8x2 – 2x – 10
x2 – 2x – 17
Multiplying Polynomials
Type of Factors
Description
*Always combine like terms!
Example
Monomial and Polynomial...

...UNIT-2
POLYNOMIALS
It is not once nor twice but times without number that the same ideas
make their appearance in the world.
1. Find the value for K for which x4 + 10x3 + 25x2 + 15x + K exactly divisible by x + 7.
(Ans : K= - 91)
4
4
2
Ans: Let P(x) = x + 10x + 25x + 15x + K and g(x) = x + 7
Since P(x) exactly divisible by g(x)
∴
r (x) = 0
x 3 + 3 x 2 + 4 x − 13
now x + 7 x 4 + 10 x 3 + 25 x 2 + 15 x + K
x 4 + 7 x3
------------3x3 + 25 x2
3x3 + 21x2
------------------4x2 + 15 x
4x2 + 28x
------------------13x + K
- 13x - 91
---------------K + 91
-----------∴ K + 91 = 0
K= -91
2. If two zeros of the polynomial f(x) = x4 - 6x3 - 26x2 + 138x – 35 are 2 ± √3.Find the
other zeros.
(Ans:7, -5)
Ans: Let the two zeros are 2 + 3 and 2 - 3
Sum of Zeros
=2+ 3 +2- 3
=4
Product of Zeros = ( 2+ 3 )(2 - 3 )
=4–3
=1
Quadratic polynomial is x2 – (sum) x + Product
11
x2 – 2x – 35
x2 – 4x + 1 x 4 − 6 x3 − 26 x 2 + 138 x − 35
x 4 − 4 x3 + x 2
-----------------2x3 – 27x2 + 138x
- 2x3 + 8x2 – 2x
-----------------------35x2 + 140x – 35
-35x2 + 140x – 35
-----------------------0
-----------------------∴ x2 – 2x – 35 = 0
(x – 7)(x + 5) = 0
x = 7, -5
other two Zeros are 7 and -5
3. Find the Quadratic polynomial whose sum and product of zeros are √2 + 1,
1
2 +1
.
Ans: sum = 2 2
Product = 1
Q.P =
X2 – (sum) x + Product
∴ x2 – (2 2 ) x + 1
4. If α,β are the zeros...

...Polynomials:
Basic Operations and Factoring
Mathematics 17
Institute of Mathematics
Lecture 3
Math 17 (Inst. of Mathematics)
Polynomials: Basic Operations and Factoring
Lec 3
1 / 30
Outline
1
Algebraic Expressions and Polynomials
Addition and Subtraction of Polynomials
Multiplication of Polynomials
Division of Polynomials
2
Factoring
Sum and Difference of Two Cubes
Factoring Trinomials
Factoring By Grouping
Completing the Square
Math 17 (Inst. of Mathematics)
Polynomials: Basic Operations and Factoring
Lec 3
2 / 30
Algebraic Expressions and Polynomials
An algebraic expression is any combination of variables and constants
involving a finite number of basic operations.
3x2 − 5yz 3
√
2x + 7y
Math 17 (Inst. of Mathematics)
Polynomials: Basic Operations and Factoring
Lec 3
3 / 30
Algebraic Expressions and Polynomials
An algebraic expression is any combination of variables and constants
involving a finite number of basic operations.
3x2 − 5yz 3
√
2x + 7y
A polynomial is an algebraic expression that is a sum of constants
and/or constants multiplied by variables raised to nonnegative integer
exponents.
5x3 − 2x4 y 2 + y 3
Math 17 (Inst. of Mathematics)
Polynomials: Basic Operations and Factoring
Lec 3
3 /...