Answer:
[tex]\text{The quotient is }2x^2+4x+6[/tex]
Step-by-step explanation:
Given the dividend and divisor we have to find the remainder using synthetic division.
The given polynomial [tex]2x^3-2x-12[/tex] is divided by (x-2).
Step 1: Set up the synthetic division.
The dividend goes on the inside of the box.
Step 2: Bring down the leading coefficient to the bottom row.
Step 3: Multiply c i.e 2 by the value just written on the bottom row.
Step 4: Add the column created in step 3 and write the sum in the bottom row.
Repeat steps 1-4 until the last column.
From the last row the remainder becomes
[tex]2x^2+4x+6[/tex]
Hence, option A is correct.
