For which value will ((s^2-1)x^8+(s+1)x^6+5) have degree (0)?

Correct answer: (s=-1)

The direct answer is option B, \(s=-1\). For degree 0, both variable terms must vanish, because only the constant 5 should remain. The coefficient of \(x^8\) is \(s^2-1\), and the coefficient of \(x^6\) is \(s+1\). At \(s=-1\), we get \((-1)^2-1=1-1=0\) and \(-1+1=0\). Hence the polynomial becomes 5, which has degree 0. Option B works exactly. Option A, \(s=1\), makes the \(x^8\) coefficient zero but gives the \(x^6\) coefficient 2, so the degree is 6. Option C, \(s=0\), gives coefficient -1 for \(x^8\), so the degree is 8. Option D, \(s=2\), leaves both higher-degree terms nonzero. A common mistake is checking only one coefficient; both must be zero.