How do you factor #6m^2+43mn-15n^2 #?
Start by knowing that we're looking for
The key to this kind of problem is to find factors for 6 and -15 that when multiplied and added all together, adds to 43. So let's do that.
Starting with the original:
We know the factors for 6 are
We know the factors for -15 are
We also know that there will be an m in the first term and an n in the second.
Overall, we're looking to find a solution in the form of:
We need a pretty big positive number for
And nice - we got it on the first go.
So we have