For the 4th week assignment, I will solve problem 90 on page 304. I will first rewrite the polynomial without parenthesis and then I will evaluate the polynomial resulting from step one, using these formula’s: P = $2000 & r = 10% and also P = $5670 & r = 3.5%. I will also be completing the problem 70 on page 311, and will show all the steps of the division. In this paper I will be using the following vocabulary words; like items, descending order, dividend, divisor, and FOIL (first, outer, inner, last). For the problem on page 304, problem 90, the problem states that the polynomial of an investment after one year that has the interest compounded semi-annually the polynomial would be: p ( 1 + r/2)2. (A.) We have to first write the polynomial without the parenthesis. (B.) Then solve for (P = 2000 + r = 10%) Part A. as well as P = $5670 + r = 3.5%) Part B. * Without parenthesis, the polynomial looks like the following: P + P r + P r2/4
The original polynomial.
The original polynomial.
I reached this by doing the following steps:
Since (1 + r/2)2, it now looks like this so that I can carry out FOIL.
Since (1 + r/2)2, it now looks like this so that I can carry out FOIL.
P(1 + r/2)2
P (1+r/2)(1+r/2)
Then you combine like terms, but since you are multiplying by 2 on r/2, it cancels out both 2’s and all you are left with is r. Then distribute the P.
Then you combine like terms, but since you are multiplying by 2 on r/2, it cancels out both 2’s and all you are left with is r. Then distribute the P.
P(1+ r/2 + r/2 + r2/4)
P(1 + 2(r/2) + r2/4)
Written in Descending order.
Written in Descending order.
P + Pr + Pr2/4
* Now to solve for P=2000 and r=10%
-------------------------------------------------
P + Pr + Pr2/4
-------------------------------------------------
2000 + 2000*(0.10) +2000* 0.102
-------------------------------------------------
4
-------------------------------------------------
2000 + 200 + 5 = $2205
-------------------------------------------------
Now I will solve problem 70 on page 311 that I have to solve and show all steps of division.
The following is the steps I took at solving the problem:
(-9x3 + 3x2 – 15x) ÷ (-3x)
The Dividend is (-9x3 + 3x2 – 15x), and the Divisor is (-3x).
The Dividend is (-9x3 + 3x2 – 15x), and the Divisor is (-3x).
-9x3 + 3x2 - 15x -3x First divide -9 by -3 which equals positive 3. And the one x on the bottom cancels one x from the top . First divide -9 by -3 which equals positive 3. And the one x on the bottom cancels one x from the top .
-9x3 + 3x2 – 15x
-3x -3x -3x
-9* x * x * x
You are now left with 3x2 for the first part of the polynomial.
You are now left with 3x2 for the first part of the polynomial.
-3 * x
-9* x * x * x
-3 * x
First divide 3 by -3, which equals -1. And the x from the bottom cancels out one of the x’s from the top.
First divide 3 by -3, which equals -1. And the x from the bottom cancels out one of the x’s from the top.
-9x3 + 3x2 – 15x
-3x -3x -3x 3 * x * x
You are now left with -1x, which simplifies to just –x, as the second part of the polynomial.
You are now left with -1x, which simplifies to just –x, as the second part of the polynomial. -3 * x
3 * x * x -3 * x
First you divide -15 by -3, which equals positive 5, and the x on the bottom cancels out the x on the top, so you do not have any x’s to carry onto the answer of the equation.
First you divide -15 by -3, which equals positive 5, and the x on the bottom cancels out the x on the top, so you do not have any x’s to carry onto the answer of the equation.
-9x3 + 3x2 – 15x
-3x -3x -3x
-15 * x
You are now left with only 5 for the last part of the polynomial, and the answer is
3x2 – x + 5.
You are now left with only 5 for the last part of the polynomial, and the answer is
3x2 – x + 5.
-3 * x
-15 * x
-3 * x
The negative sign from the -3x changes the plus sign in the equation to a minus sign, and it changes the minus sign to a plus sign in the final answer, and the equation is in Descending order.
