What is the quotient of 3x^2 + 8x + 3 divided by x + 3?

To find the quotient of the polynomial 3x² + 8x + 3 divided by x + 3, we will use polynomial long division.

1. **Set up the division**: Write 3x² + 8x + 3 under the long division symbol and x + 3 outside.

2. **Divide the first term**: Divide the first term of the dividend (3x²) by the first term of the divisor (x) to get 3x.

3. **Multiply and subtract**: Multiply 3x by x + 3 to get 3x² + 9x. Now subtract this from 3x² + 8x + 3:

• (3x² + 8x + 3) – (3x² + 9x) = -x + 3

4. **Bring down the next term**: In this case, the next term is 3. So now we have -x + 3.

5. **Repeat the process**: Divide the first term of the new dividend (-x) by the first term of the divisor (x) to get -1. Multiply -1 by x + 3 to get -x – 3.

6. **Subtract again**: Now subtract:

• (-x + 3) – (-x – 3) = 6

7. **Result**: The polynomial division of 3x² + 8x + 3 by x + 3 gives a quotient of 3x – 1 with a remainder of 6.

So, the final answer for the quotient is:

Quotient: 3x – 1, Remainder: 6