Factor the polynomial?

2x^4+4x^3+6x^2

The greatest common factor among each monomial within the polynomial is 2x², so you simply divide each piece by this number.

2x² (x² + 2x + 3)

After this, you want to factor what is in the parenthesis. What is in the parenthesis, however, is not factor-able (there are no factors of 3 that when added equal 2). So this is your final answer

2x² (x² + 2x + 3)

2x^4 + 4x^3 + 6x²