If x = 1 and x = -2 are both zeros of p(x) = x^3 + ax^2 + bx + 18, what is a + b?

Correct answer: -19

The governing concept is the zero condition p(r)=0. Because x=1 is a zero, substitute 1 into the polynomial: p(1)=1^3+a(1)^2+b(1)+18=1+a+b+18=0. Hence a+b+19=0, so a+b=-19. Therefore option A is correct. Notice that the second zero, x=-2, is not needed for the requested sum; it would be needed if the individual values of a and b were required. A common error is to omit the constant 18, producing -1 less or another nearby distractor, or to mishandle 1^3. The condition x=-2 can serve as a consistency check, but the first zero alone determines the asked quantity. Thus the answer is uniquely A.