Divide 4a2+4ab−2 by 2a . What is the quotient?(1 point)

Question

Responses

2a+2b−1
2 a plus 2 b minus 1

2a+2b−1a
2 a plus 2 b minus Start Fraction 1 over a End Fraction

2b−1a
2 b minus Start Fraction 1 over a End Fraction

2a+2b

Answer 1

To divide the expression \(4a^2 + 4ab - 2\) by \(2a\), we can do the following:

1. Start with the division: \[ \frac{4a^2 + 4ab - 2}{2a} \]

2. We can separate the terms of the numerator: \[ \frac{4a^2}{2a} + \frac{4ab}{2a} + \frac{-2}{2a} \]

3. Now, simplify each term separately:

   • The first term: \[ \frac{4a^2}{2a} = 2a \]
   • The second term: \[ \frac{4ab}{2a} = 2b \]
   • The third term: \[ \frac{-2}{2a} = -\frac{1}{a} \]

4. Combine the simplified terms: \[ 2a + 2b - \frac{1}{a} \]

Thus, the quotient of \( \frac{4a^2 + 4ab - 2}{2a} \) is: \[ 2a + 2b - \frac{1}{a} \]

The correct response from the options is: 2a + 2b - 1/a.