Answer
$-4$
Work Step by Step
$\displaystyle \lim_{x\rightarrow-1}(x^{4}-3x)(x^{2}+5x+3)=$
...Limit Law 4, limit of a product
$=\displaystyle \lim_{x\rightarrow-1}(x^{4}-3x)\lim_{x\rightarrow-1}(x^{2}+5x+3)$=
... Limit Law 2, difference, Limit Law 1, sum
$=(\displaystyle \lim_{x\rightarrow-1}x^{4}-\lim_{x\rightarrow-1}3x)(\lim_{x\rightarrow-1}x^{2}+\lim_{x\rightarrow-1}5x+\lim_{x\rightarrow-1}3)$
... Limit Law 3, constant multiple ...
$=(\displaystyle \lim_{x\rightarrow-1}x^{4}-3\lim_{x\rightarrow-1}x)(\lim_{x\rightarrow-1}x^{2}+5\lim_{x\rightarrow-1}x+\lim_{x\rightarrow-1}3)$
... Laws 9: $( \displaystyle \lim_{x\rightarrow a}x^{n}=a^{n})$, 8: ( $\displaystyle \lim_{x\rightarrow a}x=a$), and 7:($\displaystyle \lim_{x\rightarrow a}c=c$)
$=(1+3)(1-5+3)$
$=4(-1)$
$=-4$
