If the degree of ((r-10)x^{11}+(r-10)x^4+22) is (0), what is the value of (r)?

Correct answer: \(r=10\)

For the polynomial to have degree 0, it must reduce to a constant, namely 22. Therefore, the coefficients of both \(x^{11}\) and \(x^4\) must be zero. Since each coefficient is \(r-10\), we get \(r-10=0\), so \(r=10\). If \(r=-10\), the coefficient becomes \(-20\), and the polynomial still has degree 11. Exam tip: In parameter-based polynomials, first set the coefficient of the highest power to zero when checking whether the degree can decrease.