Factoring
Complex Numbers
Quadratic Formula
Solving
Mixed Skills
100
Factor completely.
2x^3+6x
2x(x^2+3)
100
Simplify
i^2
-1
100
What is the quadratic formula?
x = (-b pm sqrt(b^2-4ac))/(2a)
100
What are the solutions of this parabola?
x=-4, x=-2
100
Expand.
(2x-3)^2
4x^2 -6x+9
200
Factor completely.
x^2-3x-18
(x+3)(x-6)
200
Simplify
(8-7i)+(3-2i)
11-9i
200
Solve using the quadratic formula:
x^2+3x-1=0
(-3 pm sqrt(13))/2
200
Solve.
x^2-3x-4
x=4, x=-1
200
Solve
x^2=9
x=3 and x=-3
300
Factor completely.
2x^2+5x-3
(2x-1)(x+3)
300
Simplify
(-6-6i)-(5+5i)
-11-11i
300
Solve using the quadratic formula.
x^2+4x+5
(-4 pm 2i)/(2) = -2 pm i
300
Solve.
x^2-5=4
x=+-3
300
Simplify.
sqrt(20)
2sqrt(5)
400
Factor completely.
2x^3-8x^2+x-4
(2x^2+1)(x-4)
400
Simplify
(3+3i)(2+5i)
-9+21i
400
x^2-3x+1=0
The discriminant (b2-4ac) is positive/negative/0 (choose one) so there are ______ real solutions.
The discriminant is positive so there are 2 real solutions.
400
Solve.
(x+3)^2=16
x=1,-7
400
Solve.
x^2 = -9
x=3i and x=-3i
500
Factor completely.
x^3+ -2x^2-x+2
(x+1)(x-1)(x-2)
500
Simplify
(4+3i)(2-i)
11+2i
500
x^2 + 10x + 25=0
The discriminant (b2-4ac) is positive/negative/0 (choose one) so there are ______ real solutions.
The discriminant is 0 so there is 1 real solution.
500
Solve (Hint: you will get complex solutions)
(x-2)^2+3=-6
x=2+-3i
500
Simplify.
(x-2)^2 = -27
x=2+-3isqrt(3)