The first step is to determine the zeros of p(x).
From the Remainder Theorem,
p(a) = 0 => (x-a) is a factor of p(x), and x=a is a zero of p(x).
Try x=3:
p(3) = 3^3 - 3*3^2 - 16*3 + 48 = 27 - 27 - 48 + 48 = 0
Therefore x=3 is a zero, and (x-3) is a factor of p(x).
Perform long division.
x² - 16
-------------------------------------
x-3 | x³ - 3x² - 16x + 48
x³ - 3x²
-----------------------------------
- 16x + 48
- 16x + 48
Note that x² - 6 = (x+4)(x-4).
Therefore the complete factorization of p(x) is
p(x) = (x-3)(x+4)(x-4)
To determine when p(x) is negative, we shall test between the zeros of p(x)
x p(x) Sign
---- --------- ---------
-4 0
0 48 +
3 0
3.5 -1.875 -
4 0
p(x) is negative in the interval x = (3, 4).
Answer
The time interval is Jan. 1, 2014 to Jan. 1, 2015.
Answer: 1.5 will be on the point of 1 but just a little bit higher. -2 will be plotted exactly on -2
Step-by-step explanation:
Answer:
Choice D
Step-by-step explanation:
The distance increases at a steady rate from time = 0 to time = 1.
Then no progress is made between time = 1 and time = 2.
Then the distance increases at the same steady rate from time =2 to time = 3.
Finally, no progress is made between time = 3 and the end of the graph.
Eliminate Choices A, B and C immediately, because none of these scenarios involves a stop and wait.
That leaves only Choice D as a reasonable verbal description of what's happening here.
