what must be added to the polynomial f(x)=14x4-37x3+26x2-17x-29 so that the resulting polynomial is divided by g(x)=2x2-5x+3

On using the long division method to divide f(x) by g(x) you will get 7x^2 -x as the quotient and -14x-29 as the remainder. 

 

In order to make the f(x) divisible by g(x), the current remainder should be subtracted from the f(x). Hence, we need to subtract -14x-29 from f(x) or add 14x+29 into f(x)