MAT221 WK 4 Assignment

INSTRUCTOR GUIDANCE EXAMPLE: Week Four Assignment Financial Polynomials 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. First we are asked to rewrite the polynomial expression without any parenthesis. This means we need to FOIL the binomial (1 + r)2 and then multiply all terms by P.

P(1 + r)2 The original expression 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. Now we are to try out our polynomial formula with two different sets of numerical information. Here is the first one: P = $200 and r = 10% = .10 r given as a decimal instead of a percent P + 2Pr + Pr2 The expanded formula 200 + 2(200)(.10) + 200(.10)2 Values are substituted into the formula 200 + 40 + 200(.01) .102 = .01 and 2(200)(.10) = 40 200 + 40 + 2 200(.01) = 2 242 The final result of the formula So $200 left alone for a year at 11% compounded annually results in $242.00. Here is our second set of numerical information: P = $6780 and r = 2.5% = .025 Interest rate as a decimal number P + 2Pr + Pr2 The expanded formula 6780 + 2(6780)(.025) + 6780(.025)2 Values substituted in 6780 + 339 + 6780(.000625) .0252 = .000625 and 2(6780)(.025) = 339 6780 + 339 + 4.2375 6780(.000625) = 4.2375 7123.2375 The final result of the formula 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.

Example of dividing a polynomial by a monomial: (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 ----- – ---- – ---- Place the denominator under each term in the

–2y –2y –2y numerator . –4y3 + 3y2 + 1 Simply each term. When we divide variables with exponents, we subtract the exponents. The numbers are divided, as usual. Evaluate the + and – signs also. Since these terms are not alike, we cannot combine them, and this is the final answer. [Student should supply all the usual mechanics of the paper along with good introductory and concluding paragraphs.]