Factor by grouping. Then supply the term that is missing below.

Question

2mn-3m+8n-12= (m+4)(?-3)

The missing term
blank.

The solution is

Answer 1

To factor the expression \(2mn - 3m + 8n - 12\) by grouping, we can follow these steps:

1. Group the terms: \[ (2mn - 3m) + (8n - 12) \]

2. Factor out the common factors from each group: \[ m(2n - 3) + 4(2n - 3) \]

3. Now, we can factor out the common binomial factor \((2n - 3)\): \[ (2n - 3)(m + 4) \]

Now, we can rewrite the original expression as: \[ 2mn - 3m + 8n - 12 = (2n - 3)(m + 4) \]

Given that the question format is \((m + 4)(?-3)\), we can equate \(2n - 3\) to \(?-3\).

To determine the missing term \(?\), we can set: \[ ? = 2n \]

Thus, the full factored expression can be represented as \((m + 4)(2n - 3)\).

So, the missing term is: \[ \boxed{2n} \]

And the complete factorization of the original expression is: \[ (2n - 3)(m + 4) \]