To find the simplest form of the expression:
[tex]\[
3x \left(-x^2 + 2x + 12\right)
\][/tex]
we need to distribute [tex]\(3x\)[/tex] across the terms inside the parentheses.
First, multiply [tex]\(3x\)[/tex] by [tex]\(-x^2\)[/tex]:
[tex]\[
3x \cdot (-x^2) = -3x^3
\][/tex]
Next, multiply [tex]\(3x\)[/tex] by [tex]\(2x\)[/tex]:
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
Lastly, multiply [tex]\(3x\)[/tex] by [tex]\(12\)[/tex]:
[tex]\[
3x \cdot 12 = 36x
\][/tex]
Now, combine all these terms together:
[tex]\[
-3x^3 + 6x^2 + 36x
\][/tex]
Therefore, the simplest form of the given expression is:
[tex]\[
-3x^3 + 6x^2 + 36x
\][/tex]
So, the correct answer is:
[tex]\[
-3x^3 + 6x^2 + 36x
\][/tex]
