Question 31083
f(x)=x^3+a(x^2)+bx+2 
Since (x-2) is a factor, f(2) should be zero
f(2)=2^3+a(2^2)+2b+2=0
=>8 + 4a + 2b + 2=0
=>4a + 2b + 10 = 0
=>2(2a + b + 5) = 0
=>2a + b = -5

When divided by (x+1), the remainder is -3
=>f(-1)=-3
=>(-1)^3 + a(-1)^2 + 2b + 2 = -3
=>-1 + a + 2b + 2 = -3
=>a + 2b + 1 = -3
=>a + 2b = -4

2a + b = -5 =>b = -5 - 2a
Substituting b in the other equation a + 2b = -4 gives
a + 2(-5 - 2a) = -4
=>a - 4a = 6
=>-3a=6
=>a=-2

So, b = -5 - 2(-2) = -1

Answer: a=-2 and b=-1