On this chapter quiz for this course you can study for up to four hours If you don't study at all you will get a 70. One hour wo
uld give you an 80, the second hour increased your score to 89, the third to 92. If you studied the fourth hour your score would be 87. In which hour did diminishing returns set in? a. The second because your gain is less than the previous hour. b. The fourth because you had a drop in points in this hour. c. The third because your score peaked there. d. The first because the score was the lowest of the studying options.
If -3+5i is a solution, then by the conjugate root theorem, -3-5i is also a solution. We find the polynomial by multiplying together the factors. If x = -4, then x + 4 is the factor. If x = -3+5i, then (x-(-3+5i)) is a factor, and so is (x-(-3-5i)). Simplifying those down gives us as the first factor as (x+3-5i) and the second as (x+3+5i). We can FOIL those 2 together to get their product, and then FOIL in x+4. FOILing the 2 complex factors together gives us . If we combine like terms and cross out things that cancel it's much easier than what it looks like there! It simplifies down to . Since i^2 = -1, it simplifies further to and finally, to . Now we will FOIL in x+4. . Our final simplified third degree polynomial is