math question here....please help?

If (x-2) is a factor of f(x) then by the Factor Theorem, f(2)=0.

If f(x) gives a remainder of -3 when divided by (x+1) then by the Remainder Theorem, f(-1)=-3. So, pluggining in:

8+4a+2b+2 = 0 [f(2)= 0]

-1+a-b+2 = -3 [f(-1)= -3]

which gives the system of equations

4a+2b=-10

a - b= -4

The solution to this is a = -3, b = 1

If a binomial is a factor of the polynomial, that means that +2 in x's place will make the polynomial =0. This will be the first equation - your variables will be a & b.

The second equation comes from the other fact that you get a remainder after dividing by x+1. So, -1 in x's place will make the polynomial equal -3.

Now you have 2 equations with 2 variables - a & b. Do some simplifying of the equations (get a & b terms on one side), then solve the system of equations using either substitution methods or the addition (elimination) method.

Good Luck! :-)