Answer:
(3x^2 + 18x + 5) divided by (x + 3) using synthetic division is equal to 3x + 9.
Explanation:
To divide the polynomials (3x^2 + 18x + 5) by (x + 3) using synthetic division, we can follow these steps:
1. Set up the synthetic division table:
-3 | 3 18 5
2. Write down the coefficients of the polynomial inside the table:
-3 | 3 18 5
3. Bring down the first coefficient:
-3 | 3 18 5
3
4. Multiply the divisor (x + 3) by the result obtained and write it below the next coefficient:
-3 | 3 18 5
3 -9
5. Add the numbers in the second row:
-3 | 3 18 5
3 -9
-----
3 9
6. Repeat steps 4 and 5 until all coefficients are processed:
-3 | 3 18 5
3 -9
-----
3 9
0
7. The final row represents the coefficients of the quotient:
-3 | 3 18 5
3 -9
-----
3 9
0
8. The quotient is 3x + 9.