algebra
posted by anon .
solve the inequality express in interval notation
x^4 + 4x^3  9x^2  36x < 0

x(x^3 + 4x^2  9x  36) < 0
x( x^2(x+4)  9(x+4) ) = 0
x(x+4)(x^29) < 0
x(x+4)(x+3)(x3) < 0
so your critical values are
x = 0, 3, 4, and 3
Knowing that y = x^4 + .... is a quartic that rises in the 1st and 2nd quadrant because of the +1x^4 term, and it has 4 xintercepts, you can make a rough sketch showing a W shape with those intercepts.
It should be obvious that the graph is below the xaxis ( y < 0 ) for values between 3 and 4 or between 0 and 3
so in standard notation:
4 < x < 3 OR 0 < x < 3
I will leave it up to you to express it in interval notation 
Thank you!