Steps to factor 12x^3-9x^2+8x-6by

the polynomial cannot be factored

Step-by-step explanation:

The ratios of coefficients are 4:3 in the first and second pairs of terms, but the similarity ends there. The second pair of terms has no common factor but 2, and factoring that out leaves nothing in common with the rest of the expression:

= 3x^2 (4x - 3) + 2 (4x - 3by)

If by=1, this would factor nicely as (3x^2 + 2) (4x - 3), but that is not the case. The "by" term effectively makes the expression unfactorable.

The expression cannot be factored.