Question

Use synthetic division to divide 2a^3 + 3a + 5 by a – 3. Show all work.

2a^3 – 6a^2 + 21a + 68

2a^2 – 6a – 15 R. 50

2a^2 + 6a + 21 R. 68

Answer 1

Divide 2a^3 + 3a + 5 by a − 3 using synthetic division. Include the missing a^2 term as 0a^2.

Set k = 3 and use coefficients [2, 0, 3, 5]:

3 | 2 0 3 5
| 6 18 63
----------------
2 6 21 68

Work:
- Bring down 2.
- 3·2 = 6; add to 0 → 6.
- 3·6 = 18; add to 3 → 21.
- 3·21 = 63; add to 5 → 68 (remainder).

Quotient: 2a^2 + 6a + 21 with remainder 68.

So (2a^3 + 3a + 5) ÷ (a − 3) = 2a^2 + 6a + 21 + 68/(a − 3).

This matches the third choice: 2a^2 + 6a + 21 R. 68.