Question

Consider the function f(x)=3x^3-5x^2-88x+60-5 is a root of f(x). Find all of the roots of f(x)

Answer 1

If -5 is a root then f(x) is divisible by x + 5

The quotient from this division is 3x^2 -20x +12
Factoring this:-

= 3x^2 - 18x - 2x + 12
= 3x(x - 6) - 2(x - 6)
= (3x - 2)(x - 6)
So 2 more roots are 2/3 and 6
All the roots are -5 , 2/3 and 6.  Answer