My polynomial: $2x^3 +7x^2+12x+9$.
Now, I've tried both of the techniques given in this Wikihow page, but neither of them worked for this problem. Synthetic division is something which I think would work, but it seems like a lot of work to first use the Rational Zeros Theorem to check all the possibilities using synthetic division and then come up with a quadratic equation.
The solution given is as follows: solution in Slader.
Obviously, one cannot use synthetic division to factor our $(2x +3)$ for the division works only for factors of the form $(x-c)$. So my question is, how do you factor a polynomial like this?