One way is to work backwards.
Start with a polynomial that isn’t factorable:
3x + 5
Then multiply it by a common factor — anything you like. I’m going to pick 7x²
7x²(3x + 5)
Then also expand it out by distributing:
21x^3 + 35x²
21x^3 + 35x² – unfactored
7x²(3x + 5) – factored with GCF of 7x² brought to the front
You could also multiply two binomials and make a quadratic.
(7x + 2)(3x + 5)
7x(3x + 5) + 2(3x + 5)
= 21x² + 35x + 6x + 10
= 21x² + 41x + 10
I don’t understand the question. “GCF” stands for greatest COMMON factor, and you can’t have a common factor unless you have at least two polynomials for the factor to be common to.
Is part of the question missing?