`\frac{\left(3x^{3}+17x^{2}+21x-9\right)}{\left(x+3\right)}`
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To divide the polynomial \(3x^{3}+17x^{2}+21x-9\) by \(x+3\), we can use polynomial long division.
\[
\begin{array}{r|rrrrr}
x+3 & 3x^3 & +17x^2 & +21x & -9 & \\
\hline
& 3x^3 & +9x^2 & & & \\
\hline
& & 8x^2 & +21x & & \\
& & +8x^2 & +24x & & \\
\hline
& & & -3x & -9 & \\
& & & -3x & -9 & \\
\hline
& & & & 0 & \\
\end{array}
\]
Therefore,
\[
\frac{3x^{3}+17x^{2}+21x-9}{x+3} = 3x^{2} + 8x - 3
\]