Answer:
f(x) = (x-5)(x+2i)(x-2i)
Step-by-step explanation:
Given that
f(x)=x3−5x2+4x−20
Grouping first two terms together and second set together we have
f(x) = x^2(x-5)+4(x-5)
= (x^2+4)(x-5)
These are the factors without complex numbers of f(x)
Equate each factor to 0 to get
x-5 =0 or x^2+4=0
x =5 or x = square root of -4
i.e. x=5 or x = 2i or x =-2i (since square root of negative number is imaginary)
Factorisation is
f(x) = (x-5)(x+2i)(x-2i)
