Which polynomial has a factor of (3X - 5) along with (4X + 1)?

To determine which polynomial has both (3X - 5) and (4X + 1) as factors, we can use the fact that if a polynomial has these factors, it can be expressed as a product of these two binomials multiplied by some constant.

First, we find the product of the two factors:

(3X - 5)(4X + 1) = 12X² + 3X - 20X - 5

This simplifies to:

12X² - 17X - 5

Now we look back at the options provided. The polynomial in the first choice, 12X² - 17X - 5, matches exactly with the expression we obtained from factoring (3X - 5) and (4X + 1). This confirms that this polynomial indeed has both (3X - 5) and (4X + 1) as factors.

Polynomials B, C, and D do not yield this combination of factors when evaluated, as they do not align with the derived expression. Thus, the correct polynomial that has (3X - 5) and (4X + 1) as factors is 12X² - 17X