Question 78943: 12X^2-41X+24
Found 2 solutions by jim_thompson5910, mathdoc314:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! note: If you need help with factoring check out this solver
ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'quadratic_factoring'.
| Error occurred executing solver 'quadratic_factoring' . |
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Answer by mathdoc314(58) (Show Source):
You can put this solution on YOUR website! That is not a problem. It is an expression. There are many things that can be done with an expression. Next time I hope you will ask the question more completely and clearly!
Since you are letting me guess what is supposed to be done with it, I could graph it or solve for it = 0, but I think maybe you want me to factor it
This is going to be 
It multiplies out as 
This must be equal to
Therefore it must be  ,  , and  .
and the goal is to discover right numbers to use for a, b, c, d.
I will try to find an answer with whole numbers (no fractions or square roots yet).
a*c = 12
some possibilities are
(a=1,c=12), (a=2,c=6), (a=3,c=4), (a=4,c=3), (a=6,c=2), or (a=12, c=1).
b*d = 24
some possibilities are
(b=-1,d=-24), (b=-2,d=-12), (b=-3,d=-8), (b=-4,d=-6)
The next goal is to find the right combination of those possibilities to get a*d + b*c = -41
This can be done slowly by trying out a lot of combinations, but then you probably get tired of it and hopefully notice some patterns.
What has to happen to get -41
One thing is that a*d has to be odd or b*c has to be odd. This eliminates a lot of combinations. You can't have a and c both be even, and you can't have b and d both be even. Also you cant have a big number for a and d at the same time because it gets too far over -41 if you have things like 12*8 in it.
It turns out -41 is the smallest odd term you can get
Here are some of the details
You can work with these:(a=1,c=12), (a=3,c=4), (a=4,c=3), (a=12, c=1)
and (b=-1,d=-24), (b=-3,d=-8)
(a=4,c=3,b=-1,d=-24) -> ad+bc = -96-3 = -99
(a=4,c=3,b=-3,d=-8) -> ad+bc = -32 - 9 = -41 <-- this one is the answer
(a=12,c=1,b=-1,d=-24) -> ad+bd = -288 - 1 = -289
(a=12,c=1,b=-3,d=-8) -> ad+bd = -96 - 3 = -99
So it factors as  and I am glad that is over. There are faster answers like completing the square and the quadratic formula. I hope this is the question you wanted to ask. Next time please say what you want the tutor to do.
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