When will ((u+2)x^4+(u+2)x+15) become a constant polynomial?

Correct answer: When (u=-2)

The direct answer is B, u=−2. A constant polynomial cannot contain x⁴ or x terms, so both their coefficients must be zero. Both coefficients are u+2. Thus set u+2=0, which gives u=−2. Substitution gives (−2+2)x⁴+(−2+2)x+15=0x⁴+0x+15=15, a non-zero constant polynomial. Option A, u=2, makes u+2=4, so variable terms remain. Option B is correct because it removes both variable terms at once. Option C, u=0, gives coefficient 2, so the expression is not constant. Option D, never, is wrong because u=−2 clearly works. The key point is that the same coefficient multiplies both variable terms, so one equation removes both. Memory cue: for a constant polynomial, set every coefficient of a positive power of x equal to zero.