If the degree of ((c+7)x^9+(c^2-49)x^6+43) is (0), what is the value of (c)?

Correct answer: (c=-7)

The direct answer is option B, \(c=-7\). For degree 0, the terms with \(x^9\) and \(x^6\) must both disappear, because any surviving positive power would give degree at least 6. The coefficients are \(c+7\) and \(c^2-49\). Setting \(c=-7\) gives \(c+7=0\) and \(c^2-49=49-49=0\). The expression becomes the non-zero constant \(43\), so its degree is 0. Option A, \(c=7\), makes the second coefficient zero but leaves the first as 14, so degree 9 remains. Option B makes both coefficients zero. Option C leaves both variable terms present. Option D also leaves a non-zero \(x^9\) coefficient. Memory cue: when expressions contain \(c+a\) and \(c^2-a^2\), try \(c=-a\) to remove both terms.