How do i obtain the real number solutions to the polynomial function f(x)=x^3 - 4x^2 + x +6?

so.... notice, using the p/q factors, we ended up using 3/1 or just 3, so the root of x = 3, which gives us the factor of x-3 then

then you factor the quadratic, then set f(x) to 0, and solve each for "x"

They are somewhat similar