To simplify the expression \( 18x^2 - 12x + 63x \), first combine the like terms.
The expression can be rewritten as:
\[ 18x^2 + ( -12x + 63x) \]
Now combine the \( x \) terms:
\[ -12x + 63x = 51x \]
So, the expression simplifies to:
\[ 18x^2 + 51x \]
Next, we can factor out the common factor, which is 3:
\[ 3(6x^2 + 17x) \]
However, none of the provided options exactly match this result. Among the given options, the most simplified version can be more closely aligned to the polynomial expression.
So if we check the options, there might be a misunderstanding or constraint on the formatting of the original polynomial. None of the options given (6x3−4x2+2x, 6x−4+2x, 6x2−4x+2, 6x−2) match \( 3(6x^2 + 17x) \) or the direct simplified form.
If we are interpreting \( 63x \) to be part of \( +63x \), the simplified polynomial would remain \( 18x^2 + 51x \), and it appears that none of the listed options represent this expression correctly as is.
Thus, a review of the provided options would indicate none are correct relative to \( 18x^2 + 51x \). If you want to continue or clarify further potential constraints or different options, I'd be happy to assist!