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?

Your factoring method is fine.
In general
given a polynomial, $$P(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots +a_1 x+a_0,\quad a_n\ne0,$$ 
you can factor out the leading term when $x\ne0$:
$$
P(x)= x^n\Bigl(\,a_n+{ a_{n-1}\over x}+ \cdots +{a_1\over x^{n-1}}  +{a_0\over x^n} \,\Bigr),\quad x\ne0.
$$
When taking the limit as $x$ tends to an infinity, the parenthetical term above will tend towards $a_n$.
From this,
$$
\lim_{x\rightarrow-\infty} P(x) = \cases{\phantom{-}{\rm sign}(a_n) \infty, & n\text{ even}\cr  -{\rm sign}(a_n) \infty, & n\text{  odd}}
$$
and
$$
\lim_{x\rightarrow \infty} P(x) =  {\rm sign}(a_n)  \infty.
$$
Informally, for large $x$, a polynomial behaves as its leading term. So, to compute a limit "at infinity",  you could just drop all but the leading term of the polynomial and take the limit of just the leading term.
