1 | a b 10 -18 9 | | a a+b a+b+10 a+b-8 +--------------------------------- a a+b a+b+10 a+b-8 a+b+1
It is clear from the condition that c= 10, d= -18 and e= f(0) = 9. So, the polynomial is f(x) = ax^4 + bx^3 + 10x^2 - 18x + 9. Now, substitute x= 1 into the last expression for the polynomial and take into account that x= 1 is the root. You will get f(1) = a + b + 10 - 18 + 9 = 0, which implies a + b = -10 + 18 - 9 = -1. ANSWER