When will ((r-1)x^2+(r+2)x+5) become a constant polynomial?

Correct answer: Never

The direct answer is D, Never. A constant polynomial must have no variable term. Here the coefficients of both variable terms must therefore be zero: first, r-1=0 gives r=1; second, r+2=0 gives r=-2. One number r cannot be both 1 and -2 at the same time. The constant term 5 is already acceptable, but both variable terms must disappear. Option A, r=1, removes the x² term, but the x coefficient becomes 3, so the expression is still variable. Option B, r=-2, removes the x term, but the x² coefficient becomes -3, so it is still not constant. Option C states both values together, but one parameter cannot have two different values simultaneously; hence it is not a valid single value. Option D is correct because no single value satisfies both equations. Memory cue: for a constant polynomial, set every variable coefficient to zero and check whether all conditions have one common value.