let p be a polynomial p(x) = x^3+b*x^2+ c*x+24, where b and c are integers. Find a relation between b and c knowing that (x+2) divides p(x).

We know that (x+2) divides p(x), therefore p(x) can be written as p(x) = (x+2)q(x) + 0, where q is another polynomial of degree 2. We can calculate then p(-2): p(-2)= ((-2)+2)q(-2) = 0;p(-2)= (-2)^3+b(-2)^2+c(-2) +24=0, equivalent to p(-2)= -8+4b -2c +24=0, p(-2)= 4b-2c+16=0.Simplifying by dividing by 2: 2b-c+8=0.