y=(x+1)^2 (x-2)^3 (x+3) solve the inequality y0

Question

y=(x+1)^2 (x-2)^3 (x+3) solve the inequality y>0

anonymous · Answer

are all those being multiplied together?

anonymous · Answer

Yes

anonymous · Answer

ignore the first term, because it is always positive

anonymous · Answer

so consider only 
$$(x-2)^3(x+3)>0$$ and then note that $(x-2)^3$ is greater than zero if and only if $x-2>0$ so now consider only 
$$(x-2)(x+3)>0$$

anonymous · Answer

$(x-2)(x+3)$ is a parabola that opens up, so it is positive outside the zeros and negative between them
the zeros are $-3$ and $2$
so it is negative on $(-3,2)$ and positive on 
$$(-\infty,-3)\cup (2,\infty)$$

anonymous · Answer

oh actually if it is $y>0$ you have to exclude $-1$ as well, because at $x=-1$ it is zero also

anonymous · Answer

so maybe best to write 
$x<-3$ or $x>2$ and $x\neq -1$