Step 1 :1) Divide \(12x^3\) by \(-x\) to get \(-12x^2\)
Step 2 :2) Multiply \(-12x^2\) by \(-x+2\) to get \(12x^3 - 24x^2\) and subtract the result from \( 12x^3 - 3x + 12\) to get \( 97x^2 - 3x + 12\)
Step 3 :3) Divide \(97x^2\) by \(-x\) to get \(-97x\), multiply \(-97x\) by \(-x + 2\) to get \( 97x^2 - 194x\), and subtract the result from \(97x^2 - 3x + 12\) to get \( -169x + 12\)
Step 4 :4) Divide \(-169x\) by \(-x\) to get \(169\), multiply \(169\) by \(-x+2\) to get \(-169x + 338\), and subtract the result from \( -169x + 12\) to get \(-388\)
Step 5 :5) Combine the results: \( -12x^2 -48x^3 + 97x^2 +169x - 388 \)