Question

Which of the following options correctly represents the long division of (8x^ – 2) by (2x + 1)?

A) 4x^2 - 2x - 1 + (-1)/(2x + 1)
B) 4x^2 + 2x - 1 + (-3)/(2x + 1)
C) 4x^2 - 2x + 1 + (-3)/(2x + 1)
D) 4x^2 + 2x + 1 + (-1)/(2x + 1)

Answer 1

The correct option that represents the long division of (8x^-2) by (2x + 1) is 4x^2 - 2x + 1 + (-3)/(2x + 1).

Step-by-step explanation:

The correct option that represents the long division of (8x-2) by (2x + 1) is Option C) 4x2 - 2x + 1 + (-3)/(2x + 1).

To perform long division, we divide the numerator (8x-2) by the denominator (2x + 1). Here are the steps:

1. Start by dividing the first term of the numerator (8x-2) by the first term of the denominator (2x). This gives us 4x.
2. Multiply the entire denominator (2x + 1) by the quotient obtained in step 1 (4x). This gives us 8x2 + 4x.
3. Subtract the product obtained in step 2 from the numerator (8x-2). This gives us (-3)/(2x + 1) as the remainder.
4. Bring down the next term of the numerator (0).
5. Repeat steps 1-4 until there are no more terms in the numerator.