If the degree of (p(x)=(a+3)x^9+(a^2-9)x^6+4x^2-5) is (2), which value of (a) is correct?

Correct answer: (a=-3)

The direct answer is option B, \(a=-3\). A polynomial has degree 2 here because the terms in \(x^9\) and \(x^6\) must disappear, while the nonzero term \(4x^2\) must remain. For the \(x^9\) term, \(a+3=0\), which gives \(a=-3\). Check the \(x^6\) coefficient: \(a^2-9=(-3)^2-9=9-9=0\). The remaining polynomial is \(4x^2-5\), whose degree is 2. Option B is correct. Option A, \(a=3\), gives an \(x^9\) coefficient of 6, so the degree is 9. Option C, \(a=0\), gives coefficients 3 and -9, also leaving the degree 9 term. Option D, \(a=9\), leaves both high-degree terms. The important distinction is that degree 2 does not mean setting x equal to 2; it means all powers above 2 must vanish.