If the degree of (p(x)=(2d-6)x^4+x^2+1) is (2), what is the value of (d)?

Correct answer: 3

For the polynomial to have degree 2, the coefficient of the highest-power term \(x^4\) must be zero. Thus, \(2d-6=0\), so \(2d=6\) and \(d=3\). If \(d=2\) or \(d=4\), the coefficient of \(x^4\) is not zero, so the degree remains 4. Exam tip: In questions where the degree is reduced, first set the coefficient of the highest power equal to zero.