Factor the trinomial by grouping 6m^2-5m-4

Question

Need to factor this trinomial, and not having much luck.

Answer 1

6m²-5m-4.

 

Try to break the second term into two. Let us try to present 5m as 2m+3m.

 

6m²-3m-2m-4. Now let us group terms together.

 

(6m²-3m)-(2m+4) Factor out common factors.

 

3m(2m-1)-2(m+2). There is no way to factor further. Let us try different grouping.

 

(6m²-2m)-(3m+4)=2m(3m-1)-(3m+4) Again, no luck. 

 

Let us try this:

 

6m²-5m-4=6m²-8m+3m-4=(6m²-8m)+(3m-4)=2m(3m-4)+(3m-4). Now we got a common factor at last!

Factor (3m-4) out to obtain:

 

6m²-5m-4=(3m-4)(2m+1)