How do you factor 2x³−3x²−4x-4?
1 Answer
Explanation:
There is no easy factorization here.
There is a method to solve a cubic equation in general by hand (and calculator) on paper.
This method is based on the substitution of Vieta method.
Dividing by the first coefficient yields :
Substituting x=y+p in
if we take 3p+a=0 or p=-a/3, the first coefficient becomes zero, and we get :
(with p = 1/2)
Substituting y=qz in
if we take q = sqrt(|b|/3), the coefficient of z becomes 3 or -3, and we get :
(here q = 0.95742711)
Substituting z = t + 1/t, yields :
Substituting
A root of this quadratic equation is u=3.40983738.
Substituting the variables back, yields :
t = cuberoot(u) = 1.50514344.
z = 2.16953194.
y = 2.07716869.
The other roots can be found by dividing and solving the remaining quadratic equation.
The other roots are complex :