1. ## [SOLVED] more inequalities

I'm once again having issues solving an inequality. Any assistance would be much appreciated
$x^3-2x^2-9x-2 >= -20$

I can't simplify by grouping, as that results in
$x^2(x-2) + (-9x-2) >= -20$ which lacks a common term

and as far as I can tell, this isn't a difference or sum of cubes, so how are the critical points calculated?

2. ## Factoring

So the only way I know how to do these questions is the following:

1) Bring everything over on one side so you have:
$x^3 - 2x^2 - 9x + 18 >= 0$

2) Unfortunately, this part you just guess. Pick some numbers for x and see if one of them will cause the equation to become zero (for now we ignore the greater than).

I found that x=2 will work just dandy.

Use synthetic division or long division to factor x=2, that is, (x-2) out of that equation and you are left with a quadratic.

4) Investigate the invervals that are created and determine which ones will cause the inequality to be true.

For this question I got:

$(x-2)(x-3)(x+3) >= 0$

View this on a number line:

<----(-3)-----(2)---(3)------->

Examine x < -3, does the above give a positive or negative number, examine the next interval (i.e. -3 < x < 2) again, positive or negative number... ect..

Hope that helps

3. Yes, that's exactly what I needed. As usual, I was being blind. Once you pointed out shifting the -20 over, everything else fell into place. Thanks a lot for your time.