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.

Question

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+10x-3x-15
=2x^2+7x-15

Product=-15

(2x-5)(x+3)not this one

(2x+3)(x-5)not this one either

(2x-3)(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}

Answer 1

2x(x+5)-3(x+5)
Note that (x+5) is a common factor.
So
2x(x+5)-3(x+5)
=(x+5)(2x-3)

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

Answer 2

That works out perfectly. Thank you very much MathMate.