find the product of the roots

Question

equation:

 

y = x³ - 4x² + x + 6

Answer 1

The Rational Root Theorem says that possible solutions are factors of 6.

By trial and error 2 is a root. (8-16+2+6=0)

x-2 is a factor

(x^3-4x^2+x+6)/(x-2)=x^2-2x-3 which factors into (x-3)(x+1)

y=(x-2)(x-3)(x+1)