In addition direct substitution and the dividing out technique we also have the rationalizing technique. You will try using this technique when you see a radical in the problem.

https://www.youtube.com/watch?v=eN5BkWUE2jY&t=22s

The first technique we discussed for finding a limit analytically is direct substitution. That strategy doesn’t work when we get an indeterminate form from the substitution such as 0/0.

One strategy to handle this form is the dividing out technique. This is where you factor both the numerator and denominator and cancel any common factor.

Here are some video examples.

This example has a quadratic to factor.

The first example in this video uses a special factoring technique called difference of squares. The second example in this video avoids factoring by using synthetic division to divide out.

The second example in this video matches the 2nd example in the video above but using the special factoring technique of difference of cubes instead of using synthetic division.

This video has an example that reviews factoring trinomials with a not equal 1.