Question

Find the quotient.
(2x4 – 3x3 – 6x2 + 11x + 8) ÷ (x – 2)

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Answer 1

Using synthetic division with 2:

Coefficients: 2, -3, -6, 11, 8
Bring down 2 → multiply by 2 → 4 → add to -3 → 1
Multiply 1 by 2 → 2 → add to -6 → -4
Multiply -4 by 2 → -8 → add to 11 → 3
Multiply 3 by 2 → 6 → add to 8 → 14 (remainder)

Quotient: 2x^3 + x^2 - 4x + 3, remainder 14.

So (2x^4 − 3x^3 − 6x^2 + 11x + 8) ÷ (x − 2) = 2x^3 + x^2 − 4x + 3 + 14/(x − 2).