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8.1-8.2 : direct, inverse, joint and combined variation
8.3 : dividing polynomials
8.4 : Synthetic division
8.6-8.7 : conjugate root theorem
8.5 : the remainder and the factor theorems
100
Identify the relationship between quantities or variables as a direct variation, inverse, or neither. In a table: 2 and 12, 6 and 4, 8 and 3, 24 and 1
inverse
100
(x^2 + 6x - 10) / (x + 2)
x+4 R-18
100
(2x^3 - 4x^2 - 7x + 5) / (x + 3)
2x^2 + 2x - 1
100
Solve the equation and state the roots, the degree of equation and the number of roots. x^3 + 4x + 13 = 0
x (x^2 + 4x + 4) = 0 x (x + 2)^2 =0 roots: x = 0 , x = 2 , x = -2 degree: 3 number of roots: 3
100
Use the remainder theorem to evaluate: f(x) = 2x^3 - 7x^2 + 6x - 3 when x=3
f(x) = 6 remainder 6
200
Identify the relationship between quantities or variables as a direct variation, inverse, or neither. 1. xy=7 2. y=1.2x
1. inverse 2. direct
200
(2x^3 + x - 3) / (x + 2)
2x^2 - 4x + 9 R-21
200
(3r^4 - 6r^3 - 2r^2 + r - 6) / (r + 1)
3r^3 - 9r^2 + 7r -6
200
Solve the equation and state the roots, the degree of equation and the number of roots. x^5 - 16x = 0
x = 2i, x = -2i roots: x = 0, x = 2i, x = -2i x = 2, x = -2 degree: 5 number of roots: 5
200
Use synthetic substitution to find P(-1/3) for P(x) = 6x^3 - x^2 + 4x - 3
P(x) = -14/3
300
Identify the relationship between quantities or variables as a direct variation, inverse, or neither. y√x = 15
inverse
300
(2x^4 + 4x^3 - 5x^2 + 3x - 2) / (x^2 +2x - 3)
2x^2 + 1 R x + 1
300
(5s^3 + s^2 - 7) / (s + 1)
5s^2 - 4s + 4 R-11
300
What other roots must it have? 1) 7 - 2i 2) 3 + i - 3 + i 3) i√5, -i
1) 7 + 2i 2) 3 - i, - 3 - i 3) -i√5, i
300
Find a polynomial equation with integral coefficients that has 2, -2, and -3 (double root) as roots.
set up: P(x) = (x-2) (x+2) (x+3)^2 answer: (x^4 + 6x^3 + 5x^2 -24x - 36) / (x - 2) remainder = 0 P(2) = 0
400
r varies jointly as s and t and inversely as w. If r=20 when s=3, t=4, and w=6. Find r when s=15, t=5 and w=3.
r=k(st/w) r=250
400
(4u^4 - 4u^3 - 5u^2 - 9u - 1) / (2u - 1)
2u^3 - 2u^2 - 3u - 6 R-7
400
(x^4 - 20) / (x + 2)
x^3 - 2x^2 + 4x - 8 R-4
400
Find a cubic equation with real coefficients that has √2, i√5 as roots.
f(x) = x^3 + 5x -√2 x^2 - 5√2
400
Solve 3x^3 - x^2 - 18x + 6 = 0, given that 1/3 is a root.
x = √6, x = -√6, x = 1/3
500
The frequency of a radio wave is inversely proportional to the wavelength. If a wave 375m long has a frequency of 800 kilocycles per second, what is the length of a wave with a frequency of 2400 kilocycles per second?
f=frequency w=wavelength 375(800) = 2400f f=125 kilocycles per second
500
(x^4 - 16) / (x^2 + 3)
x^2 - 3 R7
500
(4x^3 + 2x^2 - 4x + 3) / (2x + 3)
(2x^2 - 2x + 1)(x + 2/3)
500
Completely factor f(x) = x^4 + 3x^3 - 7x^2 - 27^x - 18 given that (x + 2) and (x+1) are factors.
(x^3 + x^2 - 9x - 9) (x + 3) (x - 3)
500
Solve 2x^4 - 3x^3 - 3x - 2 = 0, given that 1/2 and 2 are roots.
x = 2, x = -1/2 , x = i, x = -i