Algebra 2-3 pg paper on Financial Polynomials

Question Description

I need an explanation for this Algebra question to help me study.


Financial Polynomials

Read the following instructions in order to complete this assignment and review the example of how to complete the math required for this assignment:

  1. Solve problem 90 on page 304 of Elementary and Intermediate Algebra. Be sure that you show all steps of the squaring of the binomial and multiplication along with any simplification which might be required.

    • Evaluate the polynomial resulting from step 1 using: 

      • P = $200 and r = 10%, and also with 
      • P = $5670 and r = 3.5% 
    • Complete problem 70 on page 311 of Elementary and Intermediate Algebra. Show all steps of the division. 
  2. Write a two- to three-page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the Instructor Guidance and be concise in your reasoning. In the body of your essay, please make sure to:

    • Demonstrate your solution to the above problems, making sure to include all mathematical work and a discussion of how and why this is applicable to your everyday life.

      • Use the underline feature with single spacing to set up the division(s), and use the “strikethrough” font to show the canceling factors. Can you think of another way this division could be approached and worked out? If yes, briefly describe the method. 
    • Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.):

      • FOIL
      • Like terms 
      • Descending order 
      • Dividend 
      • Divisor

Unformatted Attachment Preview

Running Head: FINANCIAL POLYNOMIALS Running head should use a shortened version of the title if the title is long! All capital letters for the title and the words Running and Head should be capitalized as well. Financial Polynomials (full title; centered horizontally & vertically) First Name Last Name MAT 221 Dr. XXXXXXXXX XXXXXXX Date 1 FINANCIAL POLYNOMIALS 2 Financial Polynomials Be sure to have a centered title on page 1 of your papers!! [The introductory paragraph must be written by each individual student and the content will vary depending on what the student decides to focus on in the general information of the topic. YOUR INTRODUCTION SHOULD CONNECT MATH CONCEPTS AND REAL-WORLD APPLICATIONS. DO NOT INCLUDE THE DIRECTIONS IN THE INTRO! The following paragraph is not an introduction to the paper but rather the beginning of the assignment.] On page 304, problem #89 states: “P dollars is invested at annual interest rate r for 2 years. If the interest is compounded annually then the polynomial P(1 + r)2 represents the value of the investment after 2 years” (Dugopolski, 2012). [This quote has less than 40 words so it does not need block quote.] The first part requires the polynomial expression to be rewritten without any parentheses. This means FOIL, or multiply First, Outer, Inner, Last, the binomial (1 + r)2 and then multiply all terms by P. P(1 + r)2 The original expression with the exponent ONLY with the binomial P(1 + r)(1 + r) A squared quantity multiplies itself P(1 + r + r + r2) The expression after FOIL was carried out P(1 + 2r + r2) Like terms are combined with r + r = 2r P + 2Pr + Pr2 The P is distributed across the trinomial It could also be noted that unlike traditional polynomials this one is not in descending order of the variable r, but rather in ascending order with the highest exponent in the last term instead of the first term. Additionally, this is an expression and not an equation so a solution for the variables cannot be found unless given values to use. Next, the polynomial formula with two different sets of numerical information will be solved. In these types of problems, a single numeric value will be found that represents the total. 1. P = $200 and r = 10% = .10 r given as a decimal instead of a percent FINANCIAL POLYNOMIALS 3 P + 2Pr + Pr2 The expanded formula 200 + 2(200)(.10) + 200(.10)2 Values are substituted into the formula 200 + [400(.10)] + [200(,01)] Exponents and Multiplication 200 + 40 + 2 Finish order of operations with addition 242 The final result of the formula According to the formula, $200 left alone for a year at 11% compounded annually results in $242.00. Here is the second set of numerical information: P = $6780 and r = 2.5% = .025 P + 2Pr + Pr2 Interest rate as a decimal number The expanded formula 6780 + 2(6780)(.025) + 6780(.025)2 Values substituted in 6780 + 339 + 4.2375 Order of operations and decimal rules used. 7123.2375 The final result of the formula This value must be rounded since numbers beyond the hundredths column do not apply in the existing currency system. Thus, starting with $6780 and compounding 2.5% interest once a year yields $343.24 in interest at the end of one year for a total of $7123.24. The final part of the assignment involves simplifying a polynomial expression. To do this, like terms, distributive property, and order of operations must be used. (8y4 – 6y3 – 2y) ÷ (–2y) The original expression 8y4 – 6y3 – 2y Rewrite it so that it is clear what is being divided. –2y 8y4 -6y3 -2y –2y –2y –2y . Each term must be divided by the denominator. FINANCIAL POLYNOMIALS –4y3 + 3y2 + 1 4 Simply each term. When variables with exponents are divided, we subtract the exponents. The numbers are divided as usual. Evaluate the + and – signs, also. Since these terms are not alike, they cannot be combined so the answer is simplified. [The conclusion paragraph must be written by each individual student and the content will vary depending on what the student decides to include in their summary. DO NOT INCLUDE PERSONAL NARRATIVE LIKE “I LEARNED…” OR “WE CAN DO….”. BE SURE TO SUMMARIZE WHY THE CONCEPT(S) ARE IMPORTANT AND HOW THEY CAN BE CONNECTED TO OTHER CONCEPTS.] FINANCIAL POLYNOMIALS 5 Reference Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY: McGraw-Hill Publishing. Use the word ‘Reference’ or ‘References’ as the title. THERE IS NO COLON OR UNDERLINE. Textbook should ALWAYS be included in every assignment! Be sure to use appropriate indentation (hanging), font (Arial or Times New Roman), and size (12). ...
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