15) If the identity $\left(x-\frac{3}{2}\right)^{3}+\left(x-\frac{1}{2}\right)^{3}+(x+1)^{3}+(x+2)^{3}=a x^{3}+b x^{2}+c x+d$ holds, what is the value of $a+b+c+d$? What is the value of $a+b+c+d$?
(A) $\frac{57}{4}$
(B) 9
(C) $\frac{289}{8}$
(D) 35
(E) none of the above values.
15) The answer is $(\mathbf{D})$. Since the value of a polynomial evaluated at 1 is precisely the sum of its coefficients, it suffices to substitute $x=1$ into the left-hand side of the identity, obtaining $\left(-\frac{1}{2}\right)^{3}+\left(\frac{1}{2}\right)^{3}+2^{3}+3^{3}=35$.