MATH STUCK:(
posted by Anonymous .
I am having some difficulties factoring polynomials and I use only one method to figure the stuff out, which is the guess and check method because it's just mental math work and not that complicating.
Here is a question that I know how to do, and below it I will list down the question that I do not know how to solve, and would like if you could solve it for me the way I solved the question above.
Factor:
2x(x+5)3(x+5)
=2x^2+10x3x15
=2x^2+7x15
Product=15
(2x5)(x+3)not this one
(2x+3)(x5)not this one either
(2x3)(x+5) this one is right
{So I basically used the guess and check method above after combining the like terms}
Now this is the question that left me puzzled. I would appreciate if you could solve it like the way I have done above with a simpler version.
9x^2+12xy+4y^2
{usually there is a constant in a polynomial, but this one doesn't have one, so I am cofused on what to do}

2x(x+5)3(x+5)
Note that (x+5) is a common factor.
So
2x(x+5)3(x+5)
=(x+5)(2x3)
9x^2+12xy+4y^2
with the guess and check method, you can try to see if it is a perfect square:
√(9x²)=3x
√(4y²)=2y
So try
(3x+2y)² 
That works out perfectly. Thank you very much MathMate.