Verify using algebra:
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- \(\omega\)
- So \(a\omega + b = 3\omega + 4\), hence \(a = 3\), \(b = 4\).
- Similarly, check at \(\omega^2\) (the conjugate root), but since coefficients are real, and we already matched, the remainder is \(3x + 4\).
- x^4 + 3x^3 - 2x^2 + x + 5 = (x^2 - x + 1)(x^2 + ax + b) + ax + c
- Expand right-hand side:
- = x^4 + (a - 1)x^3 + (b - a + 1)x^2 + (-b + a)x + b
