Question

Factorising 6m² - 9km + 4 - 6 a and we get ​ _________.

Option 1: (3m−2)(2m−3k+2−2a)
Option 2: (3m−2a−2)(2m−3k+2)
Option 3: (2m−3k+2)(3m−2−2a)
Option 4: (3m−2−2a)(2m−3k+2)

Answer 1

The correct factorization of the polynomial 6m² - 9km + 4 - 6a is (3m - 2)(2m - 3k + 2 - 2a), which corresponds to Option 1 among the provided choices.

Step-by-step explanation:

To factorize the polynomial 6m² - 9km + 4 - 6a, we look for two binomials that when multiplied give us back the original polynomial. We need to find factors of 6 (for the m² term) and factors of 4 (the constant term) that when combined will give us the middle term of -9km while also incorporating the -6a.

Let's take pairs of 6m² as (3m)(2m) and pairs of 4 as (4)(1). We are looking to place the factors of 4 and the -6a term in a way that will give us the middle term of -9km.

After trial and error, we find that the factorization of the given polynomial is (3m - 2)(2m - 3k + 2 - 2a). So the correct option is Option 1.

The factored form can help explain the relationships between the terms in the polynomial, breaking down the -9km into its constituent parts as influenced by the 3m and 2m from the term 6m², and combining the constant and -6a term suitably split across the two binomials.