If \(v\neq2\), what is the degree of \((v-2)x^6+x^4+1\)?

Correct answer: 6

The degree of a polynomial is the greatest power of the variable with a non-zero coefficient. Here, \(v\neq2\), so \(v-2\neq0\). Thus, the coefficient of \(x^6\) is non-zero, and the highest power of \(x\) is \(6\). Therefore, the degree is \(6\). Option \(4\) would be correct only if \(v=2\), making the \(x^6\) term vanish. Exam tip: In a polynomial involving a parameter, check the coefficient of the highest-power term first.