To simplify the expression [tex]\((2x + 1)(x^2 - 9x + 11)\)[/tex], we'll follow these steps:
1. Distribute each term in the first polynomial to every term in the second polynomial:
[tex]\[
\begin{align*}
(2x + 1)(x^2 - 9x + 11) &= 2x \cdot (x^2 - 9x + 11) + 1 \cdot (x^2 - 9x + 11) \\
&= 2x \cdot x^2 + 2x \cdot (-9x) + 2x \cdot 11 + 1 \cdot x^2 + 1 \cdot (-9x) + 1 \cdot 11
\end{align*}
\][/tex]
2. Multiply each term:
[tex]\[
\begin{align*}
2x \cdot x^2 &= 2x^3 \\
2x \cdot (-9x) &= -18x^2 \\
2x \cdot 11 &= 22x \\
1 \cdot x^2 &= x^2 \\
1 \cdot (-9x) &= -9x \\
1 \cdot 11 &= 11
\end{align*}
\][/tex]
3. Combine all the terms:
[tex]\[
2x^3 - 18x^2 + 22x + x^2 - 9x + 11
\][/tex]
4. Combine like terms:
[tex]\[
\begin{align*}
2x^3 & \quad \text{(there are no other x^3 terms)} \\
(-18x^2 + x^2) &= -17x^2 \\
(22x - 9x) &= 13x \\
11 & \quad \text{(there are no other constant terms)}
\end{align*}
\][/tex]
Therefore, the simplest form of the expression is:
[tex]\[
2x^3 - 17x^2 + 13x + 11
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{2x^3 - 17x^2 + 13x + 11}
\][/tex]
Thus, the correct choice is [tex]\( \textbf{B.} \)[/tex]
