SOLUTION: Factorise completely: 16m^2+15n-40m-6mn

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Question 745033: Factorise completely: 16m^2+15n-40m-6mn
Found 2 solutions by lenny460, KMST:
Answer by lenny460(1073) About Me  (Show Source):
You can put this solution on YOUR website!
Factorize completely: 16m^2 + 15n - 40m - 6mn

The above expression is prime. It cannot be factored.







Lennox Obuong
Algebra Tutor
Nairobi, Kenya
Email: obuong3@aol.com

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
DISCLAIMER
There may be a procedure that you were supposedly taught, but I would not know about it.

If 16m%5E2%2B15n-40m-6mn is to be the product of two factors,
both factor must include a term on m (so we could get terms with m and a term with m%5E2 too),
and just one factor must include a term in n (so we could get twems in n, but no term in n%5E2).
Let's try %28Am%2BB%29%28Cm%2BDn%29=16m%5E2%2B15n-40m-6mn.
%28Am%2BB%29%28Cm%2BDn%29=16m%5E2%2B15n-40m-6mn --> ACm%5E2%2BADmn%2BBCm%2BBDn=16m%5E2%2B15n-40m-6mn
For the expressions on the left and the right to be equivalent, all four coefficients must match:
AC=16
AD=-6
BC=-40 and
BD=15
The way I would look for answers would be setting up a tic-tac-toe grid:
My first guesses as common factors for each column are A=2 and B=5.
system%28A=2%2CAC=16%2CAD=-6%29 --> system%28C=8%2CD=-3%29 but
system%28B=5%2CBC=-40%2CBD=15%29 --> system%28C=-8%2CD=3%29 does not agree
However, If I change my guess to B=-5, I get C and D solutions that agree with the ones from A=2:
system%28B=-5%2CBC=-40%2CBD=15%29 --> system%28C=8%2CD=-3%29
So the solution is system%28A=2%2CB=-5%2CC=-8%2CD=3%29 or
16m%5E2%2B15n-40m-6mn=highlight%28%282m-5%29%288m-3n%29%29