SOLUTION: x3 + 2x^2 - 9x = 18 2x^4 + 16x Suppose the altitude of a rising hot-air balloon is given by h = 0.04 t2 + 2t, where "t" is the time in seconds after the balloon leaves the

x3 + 2x^2 - 9x = 18 
2x^4 + 16x 

Suppose the altitude of a rising hot-air balloon is given by h = 0.04 t2 + 2t, where "t" is the time in seconds after the balloon leaves the ground. How long will it take for the balloon to reach an altitude of 200 feet? 

1) x^3 + 2*x^2 - 9*x - 18 = 0
Can be re-written as


i.e.  because x^2 - 9 = (x+3)(x-3)
So the 3 roots of the equation are
x + 3 = 0 or x = -3
x - 3 = 0 or x = 3
x + 2 = 0 or x = -2

2) I assume you are looking for factorizing this expression.

2*x^4 + 16*x can be written as

 since a^3 + b^3 = (a+b)*(a^2 + b^2 - ab)

3) 
h = 0.04*t^2 + 2*t
For h = 200
200 = 0.04*t^2 + 2*t
Rewriting to remove the decimals
20000 = 4*t^2 + 200*t
Dividing by 4 and moving all terms to one side

This is a standard quadratic equation. Solved using factorization

t = -100 or t = 50
Since time cannot be negative,
t = 50 sec to achieve a height of 200 ft.
:)