Direct, Inverse, and Joint Variation
If a is directly proportional to b, and a = 3.6 when b = 10.8, find b when a = 5.
15
(12x3 - 7x2 - 14x + 5) / (3x2 + 2x - 1)
4x - 5
If P(x) = 2x3 + x2 - 3x - 2, find P (-2)
-8
x3+5x2-29x-105 = 0
If -3 is one of the roots, what are all the roots?
-3, 5, -7
List every possible rational root of 4x4+3x2-1 = 0
1, - 1, 1/2, -1/2, 1/4, -1/4
If y varies inversely as the square root of x, and if y = 2 when x = 16, find y when x = 4.
4
(x4 + 3x2 - 2x - 7)/(x2 - x - 2)
x2 + x +6 + (6x+5)/(x2 - x - 2)
If P(x) = 2x3 + 4x2 - x - 3, find P(-3)
-18
x3-5x2+36x-180 = 0
If 6i is a root, what are the roots of the equation
5, 6i, -6i
List every possible rational root of 2x3+5x2-6x-4 = 0
1, -1, 2, -2, 4, -4, 1/2, -1/2
The number of containers filled on an assembly line varies directly as the speed of the conveyor and inversely as the square of the radius of the container. If 30 5-cm containers can be filled when the speed is 2m/min, how may 3 cm container can be filled when the speed is 3m/min?
125
(6x2 + 13x - 5)/(3x - 1)
2x + 5
Is x+3 a factor of 2x3 + x2 - 3x - 2? If not, find the remainder.
NO, -38
Find a cubic equation with integral coefficients that has -4 and 3 + i as roots.
x3 - 2x2 - 14x + 40 = 0
List every possible rational root of 2x3-3x2+4x-6 = 0
1, -1, 2, -2, 3, -3, 6, -6, 1/2, -1/2, 3/2, -3/2
The volume of a cone is jointly proportional to its height and the square of the radius of its base. A cone with height 18cm and base radius 4 cm has the same volume as another cone with base radius 6 cm. What is the height of the second cone?
8 cm
(3x3 - 8x2 + x - 6) / (x - 3)
is x + 2 a factor of 2x3 + 4x2 - x - 3? If not, find the remainder
NO, -1
Find a cubic equation with integral coefficients that has -3 and 1 - 2i as roots.
x3 + x2 - x +15 = 0
Solve by first finding the rational roots:
x4-x3-2x-4 = 0
-1, 2, i*root 2, -i*root2
Ten workers can pave a stretch of road in 35 days. How many additional workers would be needed to finish the project 10 days early?
4 workers
(8x3 - x + 2)/(3 - x)
-8x2 - 24x - 71 + (215)/(3-x)
Find a polynomial equation with integral coefficients that has 1, 1/2, and 1/4 as roots.
8x3 - 14x2 + 7x - 1 = 0
List all the possibilities for the # of positive, negative, and imaginary roots of the equation x6 - 2x5 + x3 +3x2 - 4 = 0
3, 3, 0; 3, 1, 2; 1, 3, 2; or 1, 1, 4
Solve by first finding the rational roots:
2x4+3x3-7x2+3x-9=0
-3, 3/2, i, -i