3.2 Dividing Polynomials
O Long Dividing Mathed (LDM)
Divide \( 12 x^{3}-3 x+12 \) by \( -x+2 \) using 20 ñg

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: \( -12x^2 -48x^3 + 97x^2 +169x - 388 \)