To find the simplest form of the expression \((2x - 3)(3x^2 + 2x - 1)\), we'll perform polynomial multiplication. Let's break it down step-by-step.
Given:
[tex]\[
(2x - 3)(3x^2 + 2x - 1)
\][/tex]
First, distribute \(2x\) across the second polynomial:
[tex]\[
2x \cdot (3x^2 + 2x - 1) = 2x \cdot 3x^2 + 2x \cdot 2x + 2x \cdot (-1) = 6x^3 + 4x^2 - 2x
\][/tex]
Next, distribute \(-3\) across the second polynomial:
[tex]\[
-3 \cdot (3x^2 + 2x - 1) = -3 \cdot 3x^2 + -3 \cdot 2x + -3 \cdot (-1) = -9x^2 - 6x + 3
\][/tex]
Now, combine these results:
[tex]\[
6x^3 + 4x^2 - 2x - 9x^2 - 6x + 3
\][/tex]
Combine like terms:
[tex]\[
6x^3 + (4x^2 - 9x^2) + (-2x - 6x) + 3 = 6x^3 - 5x^2 - 8x + 3
\][/tex]
Thus, the simplest form of the expression is:
[tex]\[
\boxed{6x^3 - 5x^2 - 8x + 3}
\][/tex]
This corresponds to option B.
