Exam 3 245 practice Disclaimer. The actual test does not mirror this ...

Use the remainder theorem and synthetic division to find f(k).
10) k = 4 + i; f(x) = x3 + 10 10)
Solve the problem. Round to the nearest tenth unless indicated otherwise.
11) The volume of a gas varies inversely as the pressure and directly as the temperature (in
degrees Kelvin). If a certain gas occupies a volume of 2.5 liters at a temperature of 380 K
and a pressure of 20 newtons per square centimeter, find the volume when the
temperature is 456 K and the pressure is 30 newtons per square centimeter.
11)
Use the remainder theorem and synthetic division to find f(k).
12) k = -3 + 3i; f(x) = x2 + 5x + 4 12)
Use synthetic division to perform the division.
13) x 3 - 1
x - 1
13)
Solve the problem.
14) The weight that a horizontal beam can support varies inversely as the length of the
beam. Suppose that a 5-m beam can support 730 kg. How many kilograms can a 10-m
beam support?
14)
15) The current I in an electrical conductor varies inversely as the resistance R of the
conductor. The current is 5 amperes when the resistance is 719 ohms. What is the current
when the resistance is 420 ohms? Round to the nearest tenth.
15)
Solve the problem. Round to the nearest tenth unless indicated otherwise.
16) The cost of stainless steel tubing varies jointly as the length and the diameter of the
tubing. If a 5 foot length with diameter 2 inches costs $48.00, how much will a 11 foot
length with diameter 5 inches cost? Round to the nearest cent.
16)
Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
17) 2 5 ; f(x) = 5x 4 + 3x2 - 4 17)
Use the remainder theorem and synthetic division to find f(k).
18) k = -2; f(x) = x6 + 3x5 - 3x4 + 4x3 + 3x2 - 4x - 6 18)
Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k.
19) f(x) = 2x 4 - x 3 - 15x 2 + 3x; k = -3 19)
20) f(x) = 3x 3 - x 2 + 2x + 7; k = -1 20)
Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
21) 2 + i; f(x) = x 3 + 2x 2 - 6x + 8 21)
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