For this case, we have to factor the following expression:
[tex]6m ^ 2 + 25mn + 11n ^ 2[/tex]
The term that is in the middle must be rewritten as a sum of two terms whose product is:
[tex]6 * 11 = 66[/tex]
and whose sum is 25.
Those numbers are 22 and 3.
[tex]22 * 3 = 66\\22 + 3 = 25[/tex]
Rewriting the term of the medium we have:
[tex]6m ^ 2 + 3mn + 22mn + 11n ^ 2[/tex]
We factor the maximum common denominator of each group:
[tex]3m (2m + n) + 11n (2m + n)[/tex]
We factor the polynomial by factoring the maximum common denominator, [tex](2m + n)[/tex]:
[tex](2m + n) (3m + 11n)[/tex]
Answer:
[tex](2m + n) (3m + 11n)[/tex]
