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# Polynomials and Functions & Inequalities

### Polynomials

A polynomial is an algebraic expression with all variables as whole numbers (Cuemath, 2013). The whole numbers should be positive integers. It is also a mathematical statement that does not have the equal sign (=). An example of a polynomial is 5×2+6. Through this example, we can get the components of a polynomial. The coefficient is 5, x is the variable, 2 is the power, six is the constant, while 5x and 6 are the terms. Therefore, a polynomial must have all five characters to be complete.

A polynomial function is, therefore, a function we can define by calculating a polynomial. They mostly signify algebraic expressions that have specific conditions (Cuemath, 2013). An operator, a subtraction sign (-) or addition sign (+), joins the terms in the function. Additionally, we have four types of polynomial functions; quadratic, cubic, zero, and linear. A zero function could take the form of f(x) =0, while a linear function would be of the form f(x) = x+5. A quadratic function example is f(y) = 3y2-7. An example of a cubic polynomial function is f(z) = 5z3+2z2-8. Since the term polynomial is from the number of terms in it, three of them are commonly used (Cuemath, 2013). For example, monomials with one term like 2z. We also have binomials with only two terms, like a+b, and trinomials with three terms, for example, 2×4+7x-20.

We use polynomial functions in our daily lives. Mostly, the users are mathematicians. However, other professionals can use the polynomial function to get data as they perform demanding analyses in their work environment. The professionals include meteorologists and people in the construction industry.

In our daily lives, we visit places like supermarkets and malls for shopping. For instance, if we go to the stationary sector and want to buy three pens and five books, we can apply the polynomials knowledge. Let us say that the price of a book is “b” and that of a pen is “p”, prices of our commodities will be “3p+5b”. This is a polynomial function that we have applied by simply visiting a stationary sector.

Roller coaster designers would use polynomials to describe and explain the curves of their rides (Logan, 2016). The curves are a result of the application of the polynomial functions, which are used to draw graph curves. Additionally, professionals like engineers also use graph curve knowledge to construct bridges and roller coasters. Others include doctors, finding the concentration of a specific drug in the bloodstream of their patients. In the healthcare field, nurses and caregivers use polynomials to decide on particular schedules and keep records of their patients (Logan, 2016).

Furthermore, specialists in the finance and economic sector use polynomials. Through their knowledge of polynomial functions, they can interpret data in the stock market to know how prices will change in a specific period (Logan, 2016). Moreover, they can also have the ability to interpret how the prices of goods will affect their revenue. In addition, institutions that give loans need to know to calculate the present values of the loans (Logan, 2016). The calculation involves the application of polynomial functions that date back to the accumulation of interest from liquid transactions in the future.

### Functions & Inequalities

A function is a relationship between a group of inputs and acceptable outputs. We should note that each input should be related to one output (Aakash, 2019). Additionally, two pairs with a similar first element cannot exist. There are many types of functions. They include; periodic, composite, identity, constant, signum, modulus, identical, injective, and surjective functions. An elaborate example of a function is z=3x. This means that for every three units of x that you put in, you get z. Therefore, we can conclude that z is a function of x.

On the other hand, inequalities are equations that compare functions (Judah). To compare the different expressions certain signs are used. The signs are “<” that means less than, “>” meaning greater than, “≠”for not equal to, “≥” as greater than or equal to “≤” and for less than or equal to. Furthermore, inequalities have certain properties, addition, multiplication, subtraction, and division properties. A good example of inequality is (x+7) < 15. Through this example, the sign “<” has connected two functions. This means that (x+7) should be a value less than 15.

Functions and inequalities have many ways that we use them in our day-to-day activities. Functions, for instance, can be used to predict the expected growth of a specific tree or to find out the distance someone has traveled after some set time. Additionally, financial experts use functions in different ways. They include the calculation of profit from revenue and the money they can expect from certain investments. According to Ilke (2016), functions can be used to calculate the size of a population, provided the relative growth rate is constant. The author adds that functions are building blocks for activities such as curing diseases, predicting natural disasters, and designing machines.

Inequalities, on the other hand, can be used in certain situations. For example, the speed limit on our highways could be ≤ 65 km/h. In another instance, you can personally say that the number of text messages you can send in a day should be less than 200. Subsequently, an individual could make a minimum of 15% of his income to credit for some bills. Some movies also have an age restrictions. For example, before the movie starts, people under the age of sixteen should not watch that movie. Also, a person can find the time he uses to walk to different places using the inequalities knowledge. All these can be expressed mathematically using inequalities. However, we should note that inequalities do not represent the actual figure, but give a limit (Erika, 2022).

### Relevance of maths in the accounting fieldwork

I had a short conversation with my colleague, who is an accountant. I asked him about the relevance and importance of mathematics in his area of work. In this case, the area was the accounting department. He started by saying that maths is a crucial element in the accounting department. One has to know the mathematical sector to be called a good accountant (Yunker et al., 2009). The reason behind this is that accounting is deeply concerned with the measurement of transactions, of a business, which has to be very accurate. He said that an accountant should have general knowledge of numbers and calculation skills (Zandi & Shahabi, 2012).

According to the accountant, different mathematical domains are crucial in his field of work. The sectors are quantitative techniques, calculus, maths of investment, and algebra. He added that accounting has different subjects. They are; cost accounting, auditing, taxation, financial accounting, financial accounting, and managerial advisory services. All these subjects have a certain relationship with the different mathematical areas, associated with accounting.

The accountant later explained to me how the relationship occurred. Using the mathematics of investment, an accountant can calculate the compound and simple interest, and choose and analyze the best type of investment. Additionally, they can make the best choices, according to their understanding of savings, credits, investments, and purchases. Through the knowledge of business calculus, accounting experts can apply the different concepts of continuity and limits of certain functions and solve problems that are related to their business. From college algebra, accountants learn how to solve problems involving algebraic expressions and the basic procedures and concepts of algebra. Quantitative techniques helped them understand the skills to make decisions and certain values such as honesty, accountability, collaboration, and communication.

My colleague made it clear to me that mathematics was indeed an important subject in the accounting sector. Through the talk, I learned that mathematics grades are first checked to confirm if a person can study accounting as a career. Accountants can provide balanced financial statements through manipulation or a combination of figures. Additionally, they ensure that the application of balances and checks is correct in the separate branches of an organization, and they can do complete and accurate financial evaluations.

In conclusion, mathematics is an essential subject in accounting. It helps the accountants in making correct decisions, like investments. Additionally, mathematics has helped them provide balanced financial statements like the balance sheets of both group and single entities. The figures in the statements are also accurate due to calculations made possible by mathematical operations.

### Reflection on maths

Mathematics is a subject that some like and some do not. I really like mathematics. This is because it is a challenging subject and I love challenging situations in my life. Additionally, I feel like my maths teacher has played a very important role in the love I have for the subject. I have a positive relationship with the teacher. I also have a positive attitude towards the subject. Many people say that mathematics is all about the attitude. Every time I get a wrong answer in a maths problem I feel very bad. Every time a maths question is challenging i get very angry at myself. Later, I will ask my colleagues or maths teacher. Through the task, I get more knowledge and ability to perform more tasks, making maths easier for me.

Even though people are in different time zones, we all have those similar activities that we do every day. The activities help us understand the importance of maths in our daily lives. These common activities made communication between the group members to be easier, even though there were different time zones. The activities include; measuring, calculation of aspects such as discounts, rates and taxes, supplying of materials, and money exchange.

Mathematics is also applicable in our daily lives. Through the subject, we can make good choices because of our ability to think critically. This is made possible because, when solving problems, we try to get the best reasoning, look for the possible answer and interpret it to the given data. Additionally, our life becomes orderly due to the prevention of chaos.

### References

Cuemath. (2013, December 22). What are Polynomials? Definition and Examples. https://www.cuemath.com/algebra/polynomials/

Cuemath. (2013, December 22). Polynomial Function- Graph, Definition, Formulas, Types. https://www.cuemath.com/calculus/polynomial-functions/

Erika, W (2022). Equations and Inequalities: Real World Situations. https://www.elephango.com/index.cfm/pg/k12learning/lcid/12894/Equations_and_Inequalities:_Real-World_Situations#:~:text=Roads%20have%20speed%20limits%2C%20certain,represent%20values%20that%20are%20equal.

Ilke, Y. (2016, April 14). Prezi. Applications of Functions in Daily Life. https://prezi.com/bwezo45tiya0/applications-of-functions-in-daily-life/#:~:text=Functions%20are%20mathematical%20building%20blocks,output%2C%20unique%20to%20that%20function.

Logan, G. (2016, November 22). Prezi. The Use of Polynomial Functions in Real Life. https://prezi.com/ozcnjnwvoe0_/the-use-of-polynomial-functions-in-real-life/#:~:text=Since%20polynomials%20are%20used%20to,do%20cost%20analyses%2C%20for%20example.

Yunker, P. J. (2009). The influence of mathematics ability on performance in the principle of accounting. The Accounting Education Journal, 19, 1-200

Zandi, G & Shahabi, A. (2012). The relationship between mathematics and excellency and efficiency of accounting students, Journal of Modern Accounting and Auditing, 8 (10), 1419-1427

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