Question 231124
12x(squared) -8x-15
Classroom problems almost always have integer factors.  Look for a combination of coefficients that give the -8x.
12 can be 1*12, 2*6 or 3*4.  15 is 3*5. Since it's -15, the signs will be different.
Some people use a "tree", but that's just listing all possibilities.  Trial and error is quicker, imo.
12 and 1 don't look likely, I'll try 2 and 6.
(2x - 3)*(6x + 5)
-----------------
x(cubed)-125
All differences of 2 cubes have the same form:
a^3 - b^3 = (a-b)*(a^2 + ab + b^2)
--> (x-5)*(x^2 + 5x + 25)
-----------------
8x(cubed)+1
All sums of 2 cubes have the same form, also:
a^3 = b^3 = (a+b)*(a^2 - ab + b^2)
For this one, a is 2x
(2x)^3 + 1 = (2x+1)*(4x^2 - 2x + 1)
-----------------
25x(squared)+36 
This cannot be factored.  The difference can, but not the sum of 2 squares.  The sum of odd powers can be factored, but not the even powers.
email me at gsihoutx@aol.com if you have questions.