If the degree of ((c-5)x^6+(c^2-25)x^4+13) is (0), what is the value of (c)?

Correct answer: (c=5)

The direct answer is A, \(c=5\). A polynomial has degree 0 when all terms containing a positive power of \(x\) disappear and a nonzero constant remains. Here the coefficients of \(x^6\) and \(x^4\) must both be zero. First, \(c-5=0\) gives \(c=5\). Check the second coefficient: \(c^2-25=5^2-25=25-25=0\). The expression then becomes \(13\), whose degree is 0. Option A is correct because both variable terms vanish. Option B, \(c=-5\), makes \(c^2-25=0\), but \(c-5=-10\), so the \(x^6\) term remains and the degree is 6. Option C, \(c=0\), leaves nonzero coefficients, so the degree remains 6. Option D, \(c=25\), also leaves both relevant coefficients nonzero. Always check every positive-power term, not merely one coefficient.