Find limit of polynomials Suppose we  want to  find limit of the following polynomial
$$\lim_{x\to-\infty}(x^4+x^5).$$
If we directly put here $-\infty$, we   get  "$-\infty +\infty$" which is definitely undefined form, but otherwise  if factor out $x^5$, our polynomial will be of the form $x^5(1/x+1)$.
$\lim_{x\to-\infty}\frac 1x=0$, so our result will be $-\infty*(0+1)$,which equal to $-\infty$. I have exam in a 3 days and interested if  my last procedure is correct? Directly putting $x$ values  gives me undefined form, but factorization  on the other hand, negative infinity, which one is correct?

The second method is correct, since it shows that when $x$ becomes "really negative", $x^4$ will weight less than $x^5$. 
The first method is not correct, since "$-\infty+\infty$" can give anything: for example with $f(x)=x+a$ and $g(x)=-x$, where $a$ is a real number, we have $\lim_{x\to+\infty}f(x)=+\infty$, $\lim_{x\to+\infty}g(x)=-\infty$ but $\lim_{x\to+\infty}f(x)+g(x)=a$, so we can get any real number, $+\infty$ or $-\infty$ as your example shows. It's possible that $f(x)+g(x)$ doesn't converge, for example with $f(x)=x+\cos x$ and $g(x)=-x$.
