Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express the quotient P(x) / D(x) in the form P(x)/D(x)= Q(x) + R(x)/D(x). P(x)= 6x^4 - 3x^3 + 29x^2, D(x)=3x^2 + 13

Step 1 ：Since the divisor $D(x)=3x^2 + 13$ is a quadratic polynomial, we can directly use long division to divide $P(x)$ by $D(x)$.

Step 2 ：Set up the long division as follows: \[\begin{{array}}{{r|l}} 3x^2 + 13 & 6x^4 - 3x^3 + 29x^2 \end{{array}}\]

Step 3 ：Divide the leading term of the dividend $6x^4$ by the leading term of the divisor $3x^2$ to get $2x^2$. Write this term above the line.

Step 4 ：Then multiply the divisor $3x^2 + 13$ by $2x^2$ and subtract the result from the dividend $6x^4 - 3x^3 + 29x^2$ to get a new dividend $-3x^3 + 3x^2$.

Step 5 ：Repeat the process: divide the leading term of the new dividend $-3x^3$ by the leading term of the divisor $3x^2$ to get $-x$. Write this term above the line.

Step 6 ：Then multiply the divisor $3x^2 + 13$ by $-x$ and subtract the result from the new dividend $-3x^3 + 3x^2$ to get a new dividend $13x^2$.

Step 7 ：Repeat the process: divide the leading term of the new dividend $13x^2$ by the leading term of the divisor $3x^2$ to get $\frac{13}{3}$. Write this term above the line.

Step 8 ：Then multiply the divisor $3x^2 + 13$ by $\frac{13}{3}$ and subtract the result from the new dividend $13x^2$ to get a new dividend $-\frac{169}{3}$, which is the remainder.

Step 9 ：So, the quotient is $2x^2 - x + \frac{13}{3}$ and the remainder is $-\frac{169}{3}$.

Step 10 ：Finally, we can express $P(x) / D(x)$ in the form $Q(x) + R(x)/D(x)$ as follows: \[P(x) / D(x) = 2x^2 - x + \frac{13}{3} - \frac{169}{3D(x)}\]

Step 11 ：\(\boxed{P(x) / D(x) = 2x^2 - x + \frac{13}{3} - \frac{169}{3D(x)}}\)