For which value of d will the degree of (d - 1)x^4 + (d + 3)x^2 + 6 be 2?

Correct answer: d = 1

The governing concept is that a polynomial has degree 2 when its x^4 coefficient is zero while its x^2 coefficient remains non-zero. The coefficient of x^4 is d - 1, so the x^4 term disappears when d - 1 = 0, giving d = 1. At this value, the coefficient of x^2 is d + 3 = 1 + 3 = 4, which is non-zero. The expression therefore becomes 4x^2 + 6 and has degree 2. Hence option A is correct. If d = -3, the x^2 term vanishes but the x^4 coefficient is -4, so the degree is 4. For d = 0 or d = 4, the x^4 coefficient is also non-zero, so the degree remains 4. Both conditions must be checked, not just the cancellation of one term.