(x-3) is a factor of x^3+ax^2+bx-3 but when divided by x+2 the remainder is 15

Question

Solve for A and B

I know that A is 1 and B is -11, but I don't understand how to solve it

Answer 1

the easiest way is synthetic division. ivide f(x) by x-3 to see that the remainder is

9a+3b+24

divide by x+2 and the remainder is

4a - 2b - 11

so, now you have two equations to solve

3a+b+8 = 0
4a - 2b - 11 = 15

Looks like the solution above is correct

Answer 2

a=3
B=-11