Multiply the monomial by the polynomial:

[tex]\[ -2x^3(x^3 - 6x^2 - 5x + 1) \][/tex]

Choose the correct result from the following options:

A. [tex]$-2x^9 + 12x^6 + 10x^3 - 2$[/tex]

B. [tex]$-2x^6 + 8x^5 + 7x^4 - 2x^3$[/tex]

C. [tex]$-2x^6 - 12x^5 - 10x^4 - 2x^3$[/tex]

D. [tex]$-2x^6 + 12x^5 + 10x^4 - 2x^3$[/tex]

To multiply a monomial by a polynomial, you distribute the monomial across each term in the polynomial. Here's how you can do it step-by-step:

Given expression:
[tex]\[
-2x^3 \left(x^3 - 6x^2 - 5x + 1\right)
\][/tex]

### Step-by-Step Multiplication:

1. Multiply [tex]$-2x^3$[/tex] by the first term [tex]$x^3$[/tex]:
[tex]\[
-2x^3 \cdot x^3 = -2x^{3+3} = -2x^6
\][/tex]

2. Multiply [tex]$-2x^3$[/tex] by the second term [tex]$-6x^2$[/tex]:
[tex]\[
-2x^3 \cdot (-6x^2) = 12x^{3+2} = 12x^5
\][/tex]

3. Multiply [tex]$-2x^3$[/tex] by the third term [tex]$-5x$[/tex]:
[tex]\[
-2x^3 \cdot (-5x) = 10x^{3+1} = 10x^4
\][/tex]

4. Multiply [tex]$-2x^3$[/tex] by the fourth term [tex]$1$[/tex]:
[tex]\[
-2x^3 \cdot 1 = -2x^3
\][/tex]

### Combine the Results:

Now, add all these results together:
[tex]\[
-2x^6 + 12x^5 + 10x^4 - 2x^3
\][/tex]

Therefore, when you multiply the monomial [tex]$-2x^3$[/tex] by the polynomial [tex]$x^3 - 6x^2 - 5x + 1$[/tex], the result is:
[tex]\[
-2x^6 + 12x^5 + 10x^4 - 2x^3
\][/tex]