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------------------------------------------------ Factor the four-term polynomial by grouping.

[tex]12x^3 - 20x^2 + 15x - 25[/tex]

Select the correct choice below:

A. [tex]12x^3 - 20x^2 + 15x - 25 =[/tex] [tex]\square[/tex]

B. The polynomial is not factorable by grouping.

We start with the polynomial
[tex]$$
12x^3 - 20x^2 + 15x - 25.
$$[/tex]

Step 1. Group Terms

Group the polynomial into two groups:
[tex]$$
(12x^3 - 20x^2) + (15x - 25).
$$[/tex]

Step 2. Factor Common Factors in Each Group

In the first group, factor out the greatest common factor (GCF) [tex]$4x^2$[/tex]:
[tex]$$
12x^3 - 20x^2 = 4x^2(3x - 5).
$$[/tex]

In the second group, factor out the GCF [tex]$5$[/tex]:
[tex]$$
15x - 25 = 5(3x - 5).
$$[/tex]

Step 3. Factor Out the Common Binomial

Notice that both groups now contain the common factor [tex]$(3x-5)$[/tex]. Factor this binomial out:
[tex]$$
4x^2(3x-5) + 5(3x-5) = (3x-5)\left(4x^2 + 5\right).
$$[/tex]

Final Answer

Thus, the factored form of the polynomial is:
[tex]$$
12x^3 - 20x^2 + 15x - 25 = (3x-5)(4x^2+5).
$$[/tex]

Select choice A with the filled box:
[tex]$$
\boxed{(3x-5)(4x^2+5)}
$$[/tex]