For which value will ((u^2-25)x^9+(u-5)x^4+3) have degree (0)?

Correct answer: \(u=5\)

For the polynomial to have degree 0, only the constant term 3 must remain. Hence, the coefficients of both \(x^9\) and \(x^4\) must be zero. On substituting \(u=5\), \(u^2-25=25-25=0\) and \(u-5=0\), so the expression becomes 3. For \(u=-5\), the coefficient of \(x^9\) is zero, but the coefficient of \(x^4\) is \(-10\); therefore, its degree is 4. Exam tip: In degree-reduction questions, check the coefficients of every highest-power term that must vanish.