Factor the following:
-16 x^4 + x^2 + 2 x + 1
Factor -1 out of -16 x^4 + x^2 + 2 x + 1:
-(16 x^4 - x^2 - 2 x - 1)
The factors of 1 - 16 x^4 that sum to -2 are x (-4 x^2 - 1) and x (4 x^2 - 1).
So, (16 x^4 - 1) - x^2 - 2 x = -x^2 + x (-4 x^2 - 1) + x (4 x^2 - 1) + (4 x^2 - 1) (4 x^2 + 1):
-(-x^2 + x (-4 x^2 - 1) + x (4 x^2 - 1) + (4 x^2 - 1) (4 x^2 + 1))
-x^2 + x (-4 x^2 - 1) + x (4 x^2 - 1) + (4 x^2 - 1) (4 x^2 + 1) = x ((4 x^2 - 1) - x) + (4 x^2 + 1) ((4 x^2 - 1) - x):
-x (4 x^2 - x - 1) + (4 x^2 + 1) (4 x^2 - x - 1)
Factor 4 x^2 - x - 1 out of x (4 x^2 - x - 1) + (4 x^2 + 1) (4 x^2 - x - 1), resulting in (4 x^2 - x - 1) ((4 x^2 + 1) + x):
-(4 x^2 - x - 1) (4 x^2 + x + 1)
+1252 If you apply the negative sign to the parentheses, -4x^2 is less than 4x^2, right?
So a
