When will ((r+4)x^2+(r-1)x+10) become a constant polynomial?

Correct answer: Never

Direct answer: Option D, never, is correct. A constant polynomial must have no x-term or higher-power term. In the expression, the coefficient of x^2 is r + 4, so we need r + 4 = 0, giving r = −4. The coefficient of x is r − 1, so we also need r − 1 = 0, giving r = 1. One number r cannot be both −4 and 1. Therefore no value makes both variable terms disappear, and the expression cannot become constant. Option A removes the x^2 term, but leaves the x coefficient equal to −5, so the expression is still variable. Option B removes the x term, but leaves the x^2 coefficient equal to 5. Option C states both conditions together, but they are contradictory, not simultaneously possible. Option D correctly expresses the result. Exam cue: for a constant polynomial, set every coefficient of x, x^2, and higher powers to zero, then check whether one value satisfies all equations.