To simplify the expression \(18x^2 - 12x + 63x\), we first combine the like terms. The terms \(-12x\) and \(63x\) can be combined:
\[ -12x + 63x = 51x \]
Now, we rewrite the original expression:
\[ 18x^2 + 51x \]
Next, we can factor out the greatest common factor (GCF) from the expression. The GCF of \(18\) and \(51\) is \(3\):
\[ 3(6x^2 + 17x) \]
Since this factorization does not match any of the given options directly and the expression can't be simplified further in a way that matches the options, we look for any simplifications that might align closer with the provided responses.
- First option \(6x−2\) seems unrelated as the polynomial contains \(x^2\) and \(x\) terms.
- Second option \(6x^2−4x+2\) is also not equivalent.
- Third option \(6x^3−4x^2+2x\) does not make sense as we do not have a cubic term.
- Fourth option \(6x−4+2x\) doesn't resemble our expression.
From the simplifications we attempted, none of the options appear correct or equivalent to the simplified version of the original expression.
But focusing directly on \(18x^2 + 51x\) could suggest a likely error in options or an additional factorization.
In summary, the correct answer should be the aggregate we derived, which does not match the available options effectively. However, if we were just combining terms:
Final simplified form: \(18x^2 + 51x\), with potential desire for GCF factoring but that still ultimately does not align with provided option formats.