The problem asks to expand the expression $3x(x^2 - 5x + 6)$ and write the answer as a polynomial in standard form.

1. Problem Description

The problem asks to expand the expression $3x(x^2 - 5x + 6)$ and write the answer as a polynomial in standard form.

2. Solution Steps

To expand the given expression, we need to distribute the term $3x$ to each term inside the parenthesis:

$3x(x^2 - 5x + 6) = 3x(x^2) - 3x(5x) + 3x(6)$

Now, we multiply each term:

$3x(x^2) = 3x^{1+2} = 3x^3$

$3x(5x) = 3 \cdot 5 \cdot x^{1+1} = 15x^2$

$3x(6) = 3 \cdot 6 \cdot x = 18x$

Therefore, we have:

$3x(x^2 - 5x + 6) = 3x^3 - 15x^2 + 18x$

The resulting polynomial is already in standard form because the terms are arranged in decreasing order of their exponents.

3. Final Answer

$3x^3 - 15x^2 + 18x$