Final answer:
To find the quotient (2x^3 - 2x - 12) ÷ (x - 2) using division, use long division and follow the steps carefully. The final quotient is 2x^2 - 4x + 6.
Step-by-step explanation:
To find the quotient (2x^3 - 2x - 12) ÷ (x - 2) using division, you can use long division.
Step 1: Divide the first term of the dividend (2x^3) by the divisor (x - 2). The result is 2x^2.
Step 2: Multiply the divisor (x - 2) by the result from step 1, which is 2x^2. The result is 2x^3 - 4x^2.
Step 3: Subtract the product from step 2 from the dividend. The result is -4x^2 - 2x - 12.
Step 4: Repeat steps 1-3 with the new dividend (-4x^2 - 2x - 12) until you have no more terms to divide.
The final quotient is 2x^2 - 4x + 6.