When will ((v+1)x^2+(v-2)x+3) become a constant polynomial?

Correct answer: Never

The direct answer is D, Never. A constant polynomial must have zero coefficients for every term containing the variable. Here the required equations are v+1=0 and v-2=0. The first gives v=-1, while the second gives v=2. Since one value cannot be both -1 and 2, no single v can remove both variable terms. The remaining constant 3 is acceptable, but it does not solve the incompatible conditions. Option A, v=-1, removes the x² term, but the x coefficient becomes -3, so the expression still contains x. Option B, v=2, removes the x term, but the x² coefficient becomes 3, so it still contains x². Option C asks for both values simultaneously, which is impossible for one parameter. Option D is correct. Memory cue: set every variable coefficient equal to zero, then check whether the resulting values agree.