Question

the polynomial g(x)=-x^3-rx^2+2x+s has a remainder of 6 when divided by x+2 and a remainder of 119 when divided by x-3. What are the values of r and s

Answer 1

so we know from the Remainder Theorem that
g(-2) = 8-4r-4+s = 6
g(3) = -27-9r+6+s = 119
now just solve as usual