For which value will ((s^2-4)x^9+(s-2)x^7+4) have degree (0)?

Correct answer: (s=2)

The direct answer is A, \(s=2\). For the polynomial to have degree 0, the coefficients of both positive-power terms, \(x^9\) and \(x^7\), must be zero. Set the first coefficient to zero: \(s^2-4=0\), so \(s^2=4\) and \(s=2\) or \(s=-2\). Now use the second coefficient, \(s-2=0\), which gives \(s=2\). At \(s=2\), the polynomial becomes the nonzero constant 4, so its degree is 0. Option A is correct. Option B, \(s=-2\), makes the first coefficient zero but gives \(s-2=-4\), leaving an \(x^7\) term. Option C, \(s=0\), leaves both variable terms nonzero. Option D, \(s=4\), also leaves both coefficients nonzero. The important method is to impose all required coefficient conditions, not stop after solving only one equation.