Math Elementary algebra factoring by grouping help?

You are not ab idiot. It looks like you just made an typo. I do that all the time.

An example was given to me :
X2 + 2x + 8x + 16

I grouped the first and last terms just as the tutorial said
(x3 + 2x2) + (8x + 16)

You grouped well, but TYPO: x^3....Above example is X^2


X^2 + 2x + 8x + 16
(x^2 + 2x) + (8x + 16)
x (x+2) + 8 (x+2)
(x+2) (x+8)

After you group the numbers (x3+2x2) + (8x+16) you can pull out a common factor x3 and 2x2 both have x2 so it becomes x2(x+2). Then do the same for 8x+16, they have 8 in common, 8(x+2). So you get x2(x+2)+8(x+2). I assume you put x2+2x+8x+16 into the solver which would give you that answer but for the rest of the problem you used the equation x3+2x2+8x+16 which is completely different from the first.

Is it x^2 + 2x + 8x + 16 or x^3 + 2x^2 + 8x + 16 ?

x^2 + 2x + 8x + 16 = x(x + 2) + 8(x +2) = (x + 8)(x + 2)

x^3 + 2x^2 + 8x + 16 = x^2(x + 2) + 8(x +2) = (x^2 + 8)(x + 2)