Question

How do you solve `lim _ { x \rightarrow - 1} \frac { 2x ^ { 3} + 5x ^ { 2} + 4x + 1} { 3x ^ { 3} + 5x ^ { 2} + x - 1}`?

Answer 1

See below.

Explanation:

The numerator and denominator are both polynomials.

Both polynomials are `0` when `x = -1`, so `x+1` is a factor of both.

Factor by trial and error or by polynomial division, reduce the fraction, and try again to find the limit.