Question

What is the complete factorization of the polynomial function over the set of complex numbers?
f(x)=x3−5x2+4x−20
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Answer 1

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)