Question

Using synthetic division, what is the quotient (2x3 − 2x − 12) ÷ (x − 2)? 2x2 + 4x + 6 2x2 − 4x + 6 2x2 + 4x − 6 2x2 + 4x − 6 + 1 over the quantity of x minus 2

Answer 1

The answer to your question would be 2x^2+4x+6

Answer 2

`\text{The quotient is }2x^2+4x+6`

Explanation:

Given the dividend and divisor we have to find the remainder using synthetic division.

The given polynomial
`2x^3-2x-12` 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

`2x^2+4x+6`

Hence, option A is correct.