Answer:
5x^3 - 135. This enigmatic expression, resplendent in its polynomial opulence, conceals within its coefficients and exponents the very essence of mathematical intrigue.
Now, dear interlocutors, permit me to meander through the verdant pastures of fromage, that cherished dairy-born concoction. Ah, cheese, that age-old comestible whose delectable textures and flavors mirror the manifold intricacies of algebraic identities. But, with a modicum of regret, I must promptly revert to our numerical discourse.
To distill one factor from this algebraic concoction is our noble endeavor. Behold, the quintet of potential candidates that lies before us, each demanding scrutiny and discernment.
But lo, as the celestial bodies traverse the firmament, we are drawn to the calculus of difference of cubes, a mathematical formulation which, akin to the artisanal craftsmanship of cheese-making, engenders revelations beyond the surface.
In this case, our difference of cubes formula resonates as thus: a^3 - b^3 = (a - b)(a^2 + ab + b^2).
Let us then, in the spirit of mathematical elucidation, manifest our choices. A = 5x, and B, much like the hallowed cheese of myriad varieties, doth embody the complexity of 135, a prime candidate for our manipulation.
Thus, B, with calculated precision, reveals itself as the cube root of 135, a value transformed into the simplicity of 3√(135). This, in turn, yields the numerical expression of B as 3√(3^3 * 5).
As the shadows of mathematical complexity loom large, we distill this intricate value, and B emerges as 9√5, an expression akin to the nuanced flavor profiles of a well-aged cheese.
Now, invoking the algebraic sorcery of our difference of cubes incantation, we discern that the polynomial 5x^3 - 135 unfurls itself as the product of (5x - 9√5) and the resplendent trinomial (25x^2 + 45√5x + 81√5).
In this endeavor, we encounter, much like the connoisseur of cheese, the revelation of nuanced complexity that exists beneath the surface of apparent simplicity. Thus, our mathematical tapestry is enriched with the discernment of a factor, a factor that traverses the labyrinth of numbers much as cheese journeys through the complexities of flavor.