Solve Problem 90 On Page 304 Of Elementary And Intermediate

Solve problem 90 on page 304 of Elementary and Intermediate Algebra

Read the following instructions in order to complete this assignment, and review the example of how to complete the math required for this assignment: 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. 70. ( 9x 3 3x 2 15x ) (3x) 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 include: 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. Plan the logic necessary to complete the problem before you begin writing. 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. For information regarding APA samples and tutorials, visit the Ashford Writing Center, within the Learning Resources tab on the left navigation toolbar.

Paper For Above instruction

This paper presents a detailed solution to two algebraic problems from Elementary and Intermediate Algebra, along with a discussion of their practical applications in everyday life. The first problem involves algebraic expansion and evaluation, while the second focuses on polynomial division. Emphasizing clarity and mathematical accuracy, the paper also incorporates specific mathematical vocabulary to enhance understanding.

Problem 1: Algebraic Expansion and Evaluation

The first task requires squaring a binomial, which involves applying the FOIL method—multiplying each term in the binomial by the other. Consider the binomial expression (a + b)^2; expanding this gives us a^2 + 2ab + b^2. Applying this to the problem, suppose the binomial is (x + 3). Squaring this yields (x + 3)^2 = x^2 + 2 x 3 + 3^2, which simplifies to x^2 + 6x + 9.

Next, this expanded polynomial is evaluated for specific values of P and r, representing principal and rate, respectively. For P = $200 and r = 10%, the polynomial might represent compound interest calculation or growth, with the simplified form being substituted with these values: x = 200, r = 0.10. Similarly, for P = $5670 and r = 3.5%, substitution yields x = 5670, r = 0.035. These calculations illustrate how algebraic expressions model real financial scenarios.

Problem 2: Polynomial Division

The second problem involves dividing the polynomial (9x^3 + 3x^2 + 15x) by 3x. The division process begins by arranging the dividend and divisor in descending order of powers of x. The division is performed with the dividend set up under the divisor, aligning like terms for proper division. To facilitate this, the dividend and divisor are written as:

• Dividend: 9x^3 + 3x^2 + 15x
• Divisor: 3x

Using division, the first step is to divide the leading term of the dividend (9x^3) by the leading term of the divisor (3x), which gives 3x^2. This becomes the first term of the quotient. Then, multiply the divisor by this term and subtract from the dividend, which involves combining like terms and using the strikethrough method to cancel out common factors. This process is repeated until no terms remain.

An alternative approach to the division could be synthetic division if the polynomial is suitable, especially when dealing with factors of the form (x – a). For example, by re-writing the polynomial with potential roots, synthetic division can speed up the process, yet it requires the polynomial to be in a form that simplifies this technique.

Application and Discussion

These algebraic techniques are highly applicable to real-life situations, such as financial calculations, engineering design, and data analysis. For instance, understanding how to expand and evaluate polynomials helps in estimating investments' growth over time, or in analyzing patterns in data models. Polynomial division is crucial in simplifying complex expressions related to rates, speeds, or other proportional relationships encountered in daily tasks like budgeting or resource allocation.

In the algebraic division performed, the quotient reflects a simplified form of the original polynomial while revealing the relationship between variables. The operation involving the dividend and the divisor demonstrates the importance of correctly ordering and handling like terms, which ensures accurate calculations. By canceling common factors, one can efficiently reduce expressions, a technique applicable in multiple areas such as trigonometry, calculus, and even in understanding ratios in cooking or construction.

Conclusion

Mastering these algebraic methods—such as expanding binomials using FOIL, identifying like terms, and performing polynomial division—are essential skills that extend beyond mathematics into practical life. Whether calculating financial interest, analyzing data, or solving everyday problems, these techniques foster logical thinking and problem-solving skills. Additionally, exploring alternative methods like synthetic division encourages flexibility in mathematical approach, preparing students for more advanced topics in algebra and calculus.

References

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• U.S. Federal Reserve. (2022). How compound interest works. https://www.federalreserve.gov
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