When the polynomial 3x^3 +ax+ b is divided by x−2 , the remainder is 2, and when divided by x +1 , it is 5. Find the value of a and the value of b.

Insert the negative values of the divisors and put them into the polynomial. x-2 -> P(2) = 34+2a+b=2   x+1 -> P(-1)=3(-1)+(-1)a+b=5.  22+2a+b=0 -8-a+b=0, then solve the simultaneous equations and obtain the answer: a=-10, b=-2.