Algebra Practice #2

\frac{x^{24}}{24}+8 \cdot 3^{11} can be written as k \cdot A(x) \cdot B(x) \cdot C(x) \cdot D(x), where k is a rational number and A(x), B(x), C(x) and D(x) are non-constant polynomials with rational coefficients. Find the number of terms (including k) in the new form.
\frac{4}{63} \cdot (x^2+4x+3) \cdot (x+2) \cdot (x^6+4x^5) \cdot (9x^3+5) would have 10 terms.