Find the values of the constants in the following identity $2x^3+3x^2-14x-5=(ax+b)(x+3)(x+1)+C$ I'm working through identities but I can't figure out how to get further than multiplying out the above to get :
$$2x^3+3x^2-14x-5=2ax^3+3ax^2+3ax+bx^2+3bx+bx+3b+C$$
can someone give me a hint on what to do next?

Good luck in finding such constants! Let $x=-1$. The right-hand side is $0$, and the left-hand side isn't.  
Presumably there is a typo. Once it is fixed, we can go on. 
Edit: The above was a response to the question before there was a $C$ on the right. Below is a solution of the corrected problem.  
Put $x=-1$. Then the right-hand side is $C$, and the left-hand side is $10$, so $C=10$. 
Put $x=0$. The right-hand side is $3b+10$, the left is $-5$. So $3b+10=-5$, and now we know $b$.
For $a$, the coefficient of $x^3$ on the left is $2$, and on the right it is $a$.
Now we need to verify that with the $a$, $b$, and $C$ we have found, the identity actually holds. This is necessary, for all we have shown is that if there are $a$, $b$, and $c$ that satisfy the equation, then $a$, $b$, $C$ must be as calculated. But perhaps there are no $a$, $b$, $C$ with the desired property. 
Remark: Multiplying out and setting up a system of equations will get you there too, but it is somewhat tedious, and the probability of error increases. 
