Find the limit of (x^3 + 4x - 16) / (X^2 - 4) when x approaches 2?

Question

How do you do this algebraically? I tried factoring first, but the factoring doesn't seem to cancel anything out.

Answer 1

Use polynomial division. Evaluate x^3 + 4x - 16 over x^2 - 4, and you'll get

x + 8(x - 2)/(x^2 - 4).

Since x^2 - 4 = (x-2)(x+2), you'll get

x + 8/(x+2) as your new function.

Now evaluate the limit by direct substitution (x = 2) :

2 + 8/(4) = 2 + 2 = 4.

Answer 2

4