+130070 Thx, geno !!!
Note that we can write this as :
x^4 + 4x^3 - (3x^2 + 14x + 8)
x^3 ( x + 4) - (3x + 2) (x + 4) simplify as
(x + 4) ( x^3 - 3x - 2 )
Looking at the second factor, 2 is a root....so (x - 2) is also a factor
So....using sythetic division to reduce the second polynomial to a quadratic, we have
2 [ 1 0 -3 - 2 ]
2 4 2
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1 2 1 0
The remaining polynomial is x^2 + 2x + 1 which factors as (x + 1)^2
So.....the factorization is
(x + 4) ( x - 2) ( x + 1)^2
