Expert: Sherman D. - 10/2/2004

Question
1) a^3+2a^2-4a-8>0
2) 2x^3+x^2-5x<-2

Answer
1.)
a^3 + 2a^2 - 4a - 8 > 0
(a^3 + 2a^2) + (-4a - 8) > 0
a^2(a + 2) + (-4(a + 2)) > 0
a^2(a + 2) - 4(a + 2) > 0
since both the a^2 and -4 have (a + 2) in common, you can combine them to get
(a^2 - 4)(a + 2) > 0
which becomes
(a - 2)(a + 2)(a + 2) > 0

if you go from -2 to 2, you will find that those values will not make your problem higher than 0, but once you start going past 2, you will find that all values after 2, will make your problem higher than 0, so the answer is

a > 2

-----------------------------------------------------------

2.)
2x^3 + x^2 - 5x < -2
2x^3 + x^2 - 5x + 2 < 0

x < -2
or
(1/2) < x < 1

for both of these, i went to www.quickmath.com, i clicked on Solve under Inequalities, then i typed in the problem. When you have a value other than "x" you will have to type in the letter you are trying to solve for.

Sorry i couldn't be of more help, if they can't feet into a (a + b)(c + d) form, or they are not with a power of 2 of lower, i probably won't be able to help you, so all i can do is give you a helpful site.