If the degree of ((r+9)x^{10}+(r+9)x^3+18) is (0), what is the value of (r)?

Correct answer: \(r=-9\)

For the polynomial to have degree 0, it must become a constant polynomial. Therefore, the coefficients of both \(x^{10}\) and \(x^3\) must be zero. Their common coefficient is \(r+9\), so \(r+9=0\), giving \(r=-9\). The expression then becomes only \(18\), whose degree is 0. If \(r=0\), the coefficient of \(x^{10}\) is 9, so the degree remains 10. Exam tip: first check the coefficient of the term with the highest power.