To find the simplest form of the given expression [tex]\((2x - 3)(3x^2 + 2x - 1)\)[/tex], we need to expand it by multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms. Let's do this step by step.
Let’s expand [tex]\((2x - 3)(3x^2 + 2x - 1)\)[/tex]:
1. First, distribute [tex]\(2x\)[/tex]:
[tex]\(2x \cdot 3x^2 = 6x^3\)[/tex]
[tex]\(2x \cdot 2x = 4x^2\)[/tex]
[tex]\(2x \cdot (-1) = -2x\)[/tex]
2. Next, distribute [tex]\(-3\)[/tex]:
[tex]\(-3 \cdot 3x^2 = -9x^2\)[/tex]
[tex]\(-3 \cdot 2x = -6x\)[/tex]
[tex]\(-3 \cdot (-1) = 3\)[/tex]
Now, combine all the terms obtained from the distribution:
[tex]\[
6x^3 + 4x^2 - 2x - 9x^2 - 6x + 3
\][/tex]
3. Combine like terms:
[tex]\[
6x^3 + (4x^2 - 9x^2) + (-2x - 6x) + 3
\][/tex]
Simplify inside the parentheses:
[tex]\[
6x^3 - 5x^2 - 8x + 3
\][/tex]
So the simplest form of the expression [tex]\((2x - 3)(3x^2 + 2x - 1)\)[/tex] is:
[tex]\[
6x^3 - 5x^2 - 8x + 3
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{C. \ 6x^3 - 5x^2 - 8x + 3}
\][/tex]
