# Thread: Nonlinear Inequalities

1. ## Nonlinear Inequalities

The problem is to solve the inequality and write the solution set in interval notation.

(x-1)^2(x+2)^3 (greater or equal to) 0

I get that (X-1)^2 factors out to (x-1)(x+1), but I dont know how to simplify (X+2)^3 and im not sure how to go about solving the inequality.

HELP please asap. My chapter exam is tomorrow!!

2. Originally Posted by ugkwan
The problem is to solve the inequality and write the solution set in interval notation.

(x-1)^2(x+2)^3 (greater or equal to) 0

I get that (X-1)^2 factors out to (x-1)(x+1), but I dont know how to simplify (X+2)^3 and im not sure how to go about solving the inequality.

HELP please asap. My chapter exam is tomorrow!!
$(x-1)^2$ factors out to $(x-1)(x-1)$. This isn't the difference between two squares. Remember that $x^2-1=(x-1)(x+1)$, but this isn't the same as $(x-1)^2=x^2-2x+1$

There is no reason to factor it anyway, it's factored enough for you already. The only zeros of this function are $x=1$ and $x=-2$.

So now set up your test intervals to find were the function is greater than or EQUAL to zero. So you know your intervals should be closed at $x=1$ and $x=-2$. Let me know if you need more help. Lucky for you, I'll be here for a few mins.

Test intervals:

$(-\infty,-2),(-2,1),(1,\infty)$

3. Originally Posted by ugkwan
(x-1)^2(x+2)^3 (greater or equal to) 0
Since $(x-1)^2,(x+2)^2\ge0$ then we only require that $x\ge-2.$