Compare and contrast: how is factoring a trinomial ax^2+bx+c when a ≠1 different from factoring a trinomial when a=1? how is it similar?

Differences:

If the a≠1, then instead of finding two numbers that when multiplied equal c and when added equal b (which is the a=1 situation), you are looking for two numbers which when multiplied equal ac and add up to be b.

When finding the two numbers for a≠1, you cannot just plug the two numbers into (x+__)(x+__), you have to extend the b term into those two numbers.

After extending the b term into the two terms, you then have to group them and take out the GCF's unlike in an a=1 situation.

Similarities:

The first step for both is finding two terms which equal b if added.

Once factored, you have to set the factored sections to zero if you wish to find the solutions.

Before finding the two terms which equal b if added, you should take out any GCF's from the overall equation.