If f ( x ) = x 3 + 10 x 2 + 19 x − 30 f(x)=x 3 +10x 2 +19x−30 and x + 5 x+5 is a factor of f ( x ) f(x), then find all of the zeros of f ( x ) f(x) algebraically.

Answer 1

since (x+5) is a factor if you divide f(x) by (x+5) you will get the other factor which is

(x^2 +5x -6) which factors to (x-1)(x+6) so complete factorization is (x-1)(x+6)(x+5)

So zeros are at x=1,-5 and -6