If \(v\neq5\), what is the degree of \((v-5)x^8+x^4+1\)?

Correct answer: 8

Since \(v\neq5\), \(v-5\neq0\). Hence, the coefficient of \(x^8\) is non-zero, so \((v-5)x^8\) is the highest-degree term of the polynomial. Therefore, its degree is \(8\). The term \(x^4\) has degree \(4\), so it cannot determine the degree here. Exam tip: In a polynomial containing a parameter, first check whether the coefficient of the highest-power term becomes zero.