Factor Completey: f(x)= x^7 +2x^6 -8x^5 -10x^4 +19x^3 +8x^2 -12x

Any value 0f X that gives zero output when inserted in the given Eq is a solution (root). A 7 degree Eq has a

maximum of 7 solutions(roots). These
roots can be written as factors of the
Eq.

It can be found by trial and error that
the following values of X satisfies the
Eq:

X = -3, -2, -1, 0, 1, 2.
X = -3, X + 3 = 0. Repeat for all values of X and get:
F(x) = Y = (X+3)(X+2)(X+1)(X)(X-1)(X-2)
= 0.