Final answer:
To find the factors of the expression (x³-3x²-4x+12)-:(x+2), perform polynomial division and repeat until the remainder is zero.
Step-by-step explanation:
To find the factors of the expression (x³-3x²-4x+12)-:(x+2), we need to perform polynomial division.
Step 1: Divide x³ by x to get x².
Step 2: Multiply (x+2) by x² to get x³+2x².
Step 3: Subtract x³+2x² from x³-3x²-4x+12 to get -5x²-4x+12.
Step 4: Repeat steps 1-3 with -5x²-4x+12 until the remainder is zero.
The three factors of (x³-3x²-4x+12)-:(x+2) are (x²-5), (-4x-2), and 0.