use long division of polynomials to divide f(x) by x^2 - 2x - 8. note that the remainder must be zero. you will be able to solve for a and b

note that f(x) = q(x) * (x^2 - 2x - 8) = q(x) * (x - 4)(x + 2)

obviously x = 4 and x = -2 are two zeros. the last zero comes from the zero of q(x). q(x) is the quotient you get from the division you did before.

this is f(2)Find the remainder when f(x) is divided by x-2.