To simplify the expression [tex]\(-x\left(4 x^2-6 x+1\right)\)[/tex], follow these steps:
1. Distribute the [tex]\(-x\)[/tex] across each term inside the parentheses.
[tex]\[
-x \cdot 4x^2 = -4x^3
\][/tex]
[tex]\[
-x \cdot (-6x) = 6x^2
\][/tex]
[tex]\[
-x \cdot 1 = -x
\][/tex]
2. Combine these results to form the simplified expression:
[tex]\[
-4x^3 + 6x^2 - x
\][/tex]
So, the simplest form of the expression [tex]\(-x\left(4 x^2-6 x+1\right)\)[/tex] is:
[tex]\[
\boxed{-4 x^3 + 6 x^2 - x}
\][/tex]
Therefore, the correct answer is:
B. [tex]\(-4 x^3 + 6 x^2 - x\)[/tex]
