Factoring out a GCF and then a prime polynomial

The video tutorial covers the process of factoring a polynomial expression. It begins with an introduction to the importance of completing factoring problems. The teacher explains a specific problem, 3X^3 - 12X^2 - 45X, and demonstrates the initial steps in factoring by identifying the greatest common factor (GCF). The process of factoring using the GCF is detailed, and the teacher discusses the possibility of further factoring. The concept of prime factors is introduced, and the tutorial concludes with a brief mention of finding roots when further factoring is not possible.

What does it mean when an expression is described as a 'prime factor'?

What will be learned later regarding problems that cannot be factored?