What is the quotient when (x + 2) is divided into the polynomial 2x2 - 2x - 12?A.2x - 3 with a remainder of 5B.2x - 6 with no remainderC.2x - 5 with no remainderD.x + 3 with a remainder of -2SUBMITarrow_backPREVIOUS

To find the quotient when (x + 2) is divided into the polynomial 2x^2 - 2x - 12, we can use polynomial division.

Step 1: Set up the division

We write the polynomial 2x^2 - 2x - 12 inside the division symbol and (x + 2) outside.

Step 2: Divide the first term of the dividend by the first term of the divisor

We divide 2x^2 by x to get 2x, which is the first term of our quotient.

Step 3: Multiply the divisor by the first term of the quotient

We multiply (x + 2) by 2x to get 2x^2 + 4x.

Step 4: Subtract the result from the original polynomial

We subtract 2x^2 + 4x from 2x^2 - 2x - 12 to get -6x - 12.

Step 5: Divide the first term of the new polynomial by the first term of the divisor

We divide -6x by x to get -6, which is the second term of our quotient.

Step 6: Multiply the divisor by the second term of the quotient

We multiply (x + 2) by -6 to get -6x - 12.

Step 7: Subtract the result from the new polynomial

We subtract -6x - 12 from -6x - 12 to get 0.

So, the quotient when (x + 2) is divided into the polynomial 2x^2 - 2x - 12 is 2x - 6 with no remainder. Therefore, the correct answer is B. 2x - 6 with no remainder.