Question

Use factorization to simplify the given expression in part (a). Then find the indicated limit in part (b).
(a)
3x3 + 9x2 + 9x + 3
x4 + x3 + x + 1



(b)
lim
x → −1
3x3 + 9x2 + 9x + 1
x4 + x3 + x + 1

Answer 1

did you mean
3x^3 + 9x^2 + 9x + 3 ? If so, then
= 3(x+1)(x+1)(x+1)

x^4 + x^3 + x + 1
= x^3(x+1) + (x+1)
= (x+1)(x^3 + 1)
= (x+1)(x+1)(x^2 - x + 1)

so in your limit you would have

lim 3(x+1)^3 / ((x+1)^2(x^2 - x + 1) as x=-1
= lim 3(x+1)/(x^2 - x + 1)
= 0/3 = 0