Question

(3x 3 − x 2 − 7x + 6) ÷ (x + 2) synthetic division

Answer 1

Divide 3x^3 − x^2 − 7x + 6 by x + 2. For synthetic division use r = −2.

Coefficients: 3, −1, −7, 6

Synthetic process:
- Bring down 3.
- Multiply 3 by −2 → −6; add to −1 → −7.
- Multiply −7 by −2 → 14; add to −7 → 7.
- Multiply 7 by −2 → −14; add to 6 → −8 (remainder).

So the quotient is 3x^2 − 7x + 7 and the remainder is −8.

Answer: (3x^3 − x^2 − 7x + 6) ÷ (x + 2) = 3x^2 − 7x + 7 − 8/(x + 2).