Final answer:
The given polynomial expression 5a² - 30a is factored by first identifying the greatest common factor (5a), then dividing both terms by it, resulting in the factored form 5a(a - 6).
Step-by-step explanation:
The given expression to factor is 5a² - 30a. First, we identify the greatest common factor (GCF) for the terms in the expression. Both terms have a common factor of 5 and 'a', hence the GCF is 5a.
Now, we divide both terms by the GCF and write the expression as a product of the GCF and the remaining factors. This results in the factored form:
5a * (a - 6).
The expression 5a² - 30a is now factored completely, considering the greatest common factor.