Question

find the values of A and B for which x cube minus 11 X square + a x + b is exactly divisible by 8 x square - 4 x minus 5

Answer 1

polynomial , x³ +10x² + ax + b is exactly divisible by ( x -1) and (x -2) 
it means x = 1 and 2 are the zeors of given polynomial .
so, put x = 1 
(1)³ + 10(1)² +a(1) + b = 0
1 + 10 + a + b = 0
a + b = -11 --------(1)
again put x =2 
(2)³ +10(2)² +a(2) + b =0
8 + 40 + 2a + b = 0
2a + b = -48 ----------(2)
solve equations (1) and (2)
a = -37
b = 26