Question

Factor completly 2x^3+6x^2+4x+12

Answer 1

@Vlery

Answer 2

@iGreen

Answer 3

Explanation
Factor out the GCF of 2.
2x3+6x2+4x+12=2(x3+3x2+2x+6)
Now we need to factor x3+3x2+2x+6.
Because the degree of this polynomial is greater than 2 we need to use rational root test to find at least one rational zero.
Use Polynomial roots calculator (opens new window) to find rational zeros.
In this case one rational zero is x=−3.
This means that we can divide polynomial x3+3x2+2x+6 with x+3 (the factor theorem)
After division we have: (you can use Synthetic Division Calculator for the step-by-step explanation on how to divide polynomials. )
x3+3x2+2x+6x+3=x2+2
that is
x3+3x2+2x+6=(x+3)(x2+2)
x2+2 cannot be factored further because it has no rational zeroes.