What is the complete factorization of the polynomial function over the set of complex numbers? f(x)=x3−5x2+4x−20 enter your answer in the box.

f(x)=(x-2)(x+2)(x-5)

Step-by-step explanation:

f(x)=x³-5x²+4x-20                 1. Just group randomly

f(x)=x²(x-5)+4(x-5)                2. Factor the groupings

f(x)=(x²+4)(x-5)                      

f(x)=(x-2)(x+2)(x-5)                3. Factor the difference of two squares

 is the required factorization of f(x).

Step-by-step explanation:

To factor the expression we must first group the terms and then take out common from these groups

Taking common from first group and the 4 from second group we get:

Now, to factor in complex from we have to break term

As,

Also using identity

On solving

 is the required factorization of f(x).

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step-by-step explanation: