I have a question about graphing a polynomial. I don't know how to find the zeros, asimptote and other information to graph the following polynomial: $$\lvert(x^2(x+3)-10x-24)\rvert$$
How to factorize the polynomial and how to find all other information. Thank you very much.
Guide:
Focus on the polynomial inside the absolute sign.
$$p(x)=x^3+3x^2-10x-24$$
By rational root test (try out factors of $24$), we can see that $x=-2$ is a root and hence $(x+2)$ is a factor of the polynomial. Hence we can write $p(x)=(x+2)q(x)$ where $q(x)$ is a quadratic function.
After finding out the root of $p(x)$, note that $\lim_{x \to \infty} p(x)=\infty$ and $\lim_{x \to -\infty} p(x)=-\infty.$
With that you can sketch $p(x)$, to sketch $|p(x)|$, if you see $p(x)$ take negative value, flip the graph to make it positive.