Complex Numbers
Synthetic Substitution/Long Division
Maximize/Minimize Inequalities
Quadratic Formula/Completing the Square
Factoring
100
Simplify: 3i^2 + i
3 + i
100
Given: -x^4 - 3x^3 + 5x^2 - 1/2x + 1 ; f(-2) Find Remainder.
f(-2) = 30
100
Using the chart, give an inequality that shows the minimum number of each TV that must be produced.
x ≥ 0 ; y ≥ 0
100
Complete the Square: x^2 - x = 5
X = 1/2 ± √21/2 ("1/2" plus or minus square root of "21" over "2")
100
Factor: F(x)=x^4 - 9x^2 + 4x + 12 given that (x-2) and (x+1) are factors.
f(x) = (x-2)^2 (x+1)(x+3)
200
Simplify: -3 + 4i/i ("-3 + 4i" over "i")
4 + 3i
200
Use Synthetic Substitution: f(x)= 2x^4 - 3x^2 +2x - 1 ; find f(3i)
f(3i)= 188 + 6i
200
Using the chart, give an inequality that shows the quantity of each TV that can be produced by Machine A.
X + 2y ≤ 16
200
Solve Either Way: x^2 + 8x = -12
-2 and -6
200
Factor: f(x)=x^3 + 7x^2 + 2x - 40 given that (x+5) is a factor.
f(x)= (x+5) (x-4) (x+2)
300
Simplify: 2-3i / -2+5i ("2-3i" over "-2+5i")
-19 - 4i / 29 ("-19-4i" over "29")
300
Find: (3x^3 + 19x^2 - 13x + 23) ÷ (x + 7)
3x^2 - 2x + 1 + 16/x+7
300
Using the chart, give an inequality that shows the quantity of each TV that can be produced by Machine B.
X + Y ≤ 9
300
Solve Either Way: x / x-3 = 1-x / x+2 (X over "x - 3" = "1 - x" over "x + 2")
1/2 ± i√5 / 2 (One-half plus or minus "i√5" over 2)
300
Factor: Factor: f(x)= x^4 - 2x^3 + 2x - 1
f(x)= (x-1)^3 (x+1)
400
Simplify: (3/2 + 5/2i) - (5/3 - 11/3i)
-1/6 + 37/6i
400
Use Synthetic Substitution: f(x)= x^3 - x + 5 ; find f(1-√2)
f(1-√2)= 11 - 4√2
400
Using the chart, give an inequality that shows the quantity of each TV that can be produced by Machine C.
4x + y ≤ 24
400
Use Quadratic Formula (Leave answer in terms of square root) -5x^2 - 3x +9 = 0
X = 3 ± 3√21 / -10 (3 plus or minus "3√21" over "-10")
400
Find a cubic function with roots 3 and 5i.
x= 3, 5i, -5i f(x) = x^3 - 3x^2 + 25x - 75
500
Simplify: 3i (5 - 2i) - (5i + 2)
3 + i
500
Use Long Division: (x^3 - 5x^2 - 4x + 23) ÷ (x-2)
x^2 - 3x - 10 + 3/x+2
500
If the company makes a $60 profit on each console TV and a $40 profit on each portable TV, determine the number of console and portable TVs the company should use the maximize the profit. (Give an equation)
P = 60x + 40y
500
Solve Either Way: x - 3 = √30-2x
X = 7
500
Find a quintic function with roots 1, i, and √2.
x = 1, i, -i, √2, -√2 f(x)= x^5 - x^4 - x^3 + x^2 - 2x + 2
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