Given one zero of f(x)=x^3-2x^2-5x+6 to be 1 this means that x-1 is a factor of the polynomial x³-2x²-5x+6
Before we can get the other two factors. We need to divide the polynomial function by x-1 and factorize the resulting quotient as shown in the attachment.
Quotient Q(x) = x²-x-6
Factorizing this function
x²-3x+2x-6 = 0
x(x-3)+2(x-3) = 0
(x+2)(x-3) = 0
x+2 = 0 and x-3 = 0
x = -2 and x= 3
Therefore the other zeros of the function are -2 and 3
