Limits with Indeterminate Forms Problem 1 (Calculus 1)

This is the first of many problems on evaluating limits with indeterminate forms of the type 0/0. These pop up all throughout the calculus sequence but especially with what's coming soon in calculus 1, the limit definition of the derivative. We point out the four standard algebraic tricks that can used to eliminate the indeterminate form: factoring, expanding, using the conjugate, and common denominators. For this problem we try factoring.

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► Artist Attribution
Music By: "After The Fall"
Track Name: "Pieces"
Music Published by: Chill Out Records LLC
License: Creative Commons Attribution 4.0 International (CC BY - 4.0)

[joeanava]

can you explain how did you get the 8 and -3?

[khadijaSallau]

It was -8 and +3, but you changed it when putting it in the equation. Why? Is it allowed because you want to cancel out?