Checking answers - limit problems?

Question

I asked for help before and it really helped so thank you guys!
I want to see if I did these right:
1) lim x-->-1 (t^2+1)^3*(t+3)^5 and we had to use a limit law and state which one. I used the product rule.
I got: lim x-->-1 (t^2+1)^3 * lim x-->-1 (t+3)^5
= lim x-->-1 (t^2+1) * lim x-->-1 (t^2+1) * lim x-->-1 (t^2+1) * lim x-->-1 (t+3) * lim x-->-1 (t+3) * lim x-->-1 (t+3) * lim x-->-1 (t+3) * lim x-->-1 (t+3)
= (by pluggin in -1 for t) 2*2*2*2*2*2*2*2 = 256

2) lim x-->-1 (x^2+2x+1) / (x^4-1)
= (by factoring) lim x-->-1 (x+1)(x+1) / (x^2-1)(x^2+1)
= Then by factoring (x^2-1) = lim x-->-1 (x+1)(x-1) / (x-1)(x+1)(x^2+1)
= then canceling out the (x+1) from the top and bottom = lim x-->-1 (x+1) / (x-1)(x^2+1)
= (pluggin in -1) lim x-->-1 (x+1) / (x-1)(x^2+1) = (-1)+1 / (-1-1)(-1^2+1) = 0 / (-2)(2) = 0 / -4 = 0

Answer 1

1) By far the simplest way is to note that this is a polynomial, hence continuous, so the limit is just the value at -1 which is
((-1)^2+1)^3 (-1+3)^5 = 2^3 . 2^5 = 2^8 = 256.
I don't see any need to break each term down into its component linear factors - even if you want to use the product rule, I'd only go as far as lim x-->-1 (t^2+1)^3 * lim x-->-1 (t+3)^5 before substituting -1 in.

2) Correct except for a typo in the third line - should be (x+1)(x+1) on the top.