Answer:
(m - 6n)(3m + 2n)
Explanation:
Given
3m² - 16mn - 12n²
Consider the factors of the product of the coefficient of the m² term and the n² term which sum to give the coefficient of the mn term
product = 3 × - 12 = - 36 and sum = - 16
The factors are - 18 and + 2
Use these factors to split the mn term
3m² - 18mn + 2mn - 12n² ( factor the first/second and third/fourth terms )
= 3m(m - 6n) + 2n(m - 6n) ← factor out (m - 6n) from each term
= (m - 6n)(3m + 2n)