SOLUTION: I am a mom trying to recall my high school math to help my son. I am having trouble factoring these problems: 12x(squared) -8x-15 x(cubed)-125 8x(cubed)+1 25x(squared)+

Question 231124: I am a mom trying to recall my high school math to help my son. I am having trouble factoring these problems:
12x(squared) -8x-15
x(cubed)-125
8x(cubed)+1
25x(squared)+36
Help!! and thanx
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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.
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