Polynomial division and financial applications in algebra

Financial Polynomials

Solution for the problem: (-9x3 + 3x2 -- 15x)

The division process for the polynomial above can be approached in the same way as dividing whole numbers. The polynomial (-9x3 + 3x2 -- 15x) is the dividend, while (-3x) is the divisor. To easily facilitate the division process, the whole equation will be multiplied by "-1." The new equation is: (9x3 -- 3x2 + 15x) / (3x). Writing the question in long division form, begin dividing (9x3) first by (3x), which is equal to (3x2). To cancel the first part of the equation, the first part of the quotient must be negative. Thus, 3x2 becomes (-3x2). Place (-3x2) above the division bracket as shown below.

) 9x3-3x2 + 15x

Multiply (3x) by (-3x2), which is equal to 9x3. Placing 9x3 below (-9x3) then subtract them, resulting to zero. The remaining parts of the equation must be divided in a descending order. Bring down the next term, (-3x2), and divide again by the divisor 3x. Dividing (-3x2) by 3x will give the quotient x. This is placed above the division bracket and added to the equation, resulting to the yet unfinished quotient:

____- 3x2 + x

3x

) 9x3-3x2 + 15x

-9x3

P (1 + r/2)2 = P (1 + r/2) (1 + r/2)

Then, using the FOIL method (first terms are multiplied first, outer terms next, then inner, and last terms), the polynomial will be converted to a polynomial without parentheses .

P (1 + r/2 + r/2 + r2/4)

Combining/adding like terms r/2 and r/2 in the equation above results to the equation: P (1 + 2r/2 + r2/4)

Canceling "2" in 2r/2 (as 2/2 will give a quotient of 1), the resulting polynomial is P (1 + r + r2/4). Using distributive law, the final solution to the polynomial is: P + Pr + Pr2/4.

B1. Using the polynomial P + Pr + Pr2/4, the following values for P. And r will be plugged in: P = $200 and r = 10%

P + Pr + Pr2/4 = $200 + $200 (.10) + ($200) ((.10)2 / 4)

= $200 + $200 (.10) + ($200) ((.01)/4)

= $200 + $20 + 2/4

= $200 + $20 + 1/2

= $200 + $20 + .5

= $220.5

B2. Using the polynomial P + Pr + Pr2/4, the following values for P. And r will be plugged in: P = $5,670 and r = 3.5%

P + Pr + Pr2/4 = $5,670 + $5,670 (.035) + ($5,670) ((.035)2 / 4)

= $5,670 + $198.45 + ($5,670) ((.001225)/4)