Question

What is the quotient of (x³ + 3x² + 5x + 3/x + 1)?

A) (x² + 2x + 3)
B) (x² + 2x + 2)
C) (x² + 3x + 2)
D) (x² + 3x + 3)

Answer 1

To find the quotient of (x³ + 3x² + 5x + 3) divided by (x + 1), you can use polynomial long division. The final quotient is x² + 2x + 3.

Step-by-step explanation:

To find the quotient of (x³ + 3x² + 5x + 3) divided by (x + 1), we can use polynomial long division. Here are the steps:

1. Divide the first term of the dividend (x³) by the first term of the divisor (x) to get x².
2. Multiply the divisor (x + 1) by the quotient term (x²) to get x³ + x².
3. Subtract x³ + x² from the dividend (x³ + 3x² + 5x + 3) to get 2x² + 5x + 3.
4. Repeat the process with the new dividend (2x² + 5x + 3) and the same divisor (x + 1).
5. Divide the first term of the new dividend (2x²) by the first term of the divisor (x) to get 2x.
6. Multiply the divisor (x + 1) by the new quotient term (2x) to get 2x² + 2x.
7. Subtract 2x² + 2x from the new dividend (2x² + 5x + 3) to get 3x + 3.
8. Repeat the process with the new dividend (3x + 3) and the same divisor (x + 1).
9. Divide the first term of the new dividend (3x) by the first term of the divisor (x) to get 3.
10. Multiply the divisor (x + 1) by the new quotient term (3) to get 3x + 3.
11. Subtract 3x + 3 from the new dividend (3x + 3) to get 0.

The final quotient is x² + 2x + 3. Therefore, the correct answer is option A) (x² + 2x + 3).