Answer:
To find the quotient and remainder for the polynomial \( \frac{2x^2 + 9x + 5}{x + 2} \), you can use polynomial long division.
Let's go through the steps:
1. Divide the leading term of the numerator by the leading term of the denominator. In this case, \( \frac{2x^2}{x} = 2x \).
2. Multiply the entire denominator by the result from step 1 and subtract it from the numerator. You get \( 2x^2 + 4x \).
3. Bring down the next term from the numerator, which is \( 9x \).
4. Repeat steps 1-3 until you can't divide anymore.
The quotient is \( 2x + 5 \) and the remainder is \( -5 \). Therefore, the division is \( 2x + 5 - \frac{5}{x+2} \).