contestada

what is the complete factorization of the polynomial below
x^3-4x^2+x-4?

A. (x-4)(x+i)(x-1)
B. (x+4)(x+i)(x-i)
C. (x+4)(x-i)(x-i)
D. (x-4)(x-i)(x-i)

Respuesta :

kudzordzifrancis

Answer:

B. (x+4)(x+i)(x-i)

Step-by-step explanation:

Let [tex]P(x)=x^3-4x^2+x-4[/tex]

We can factor this polynomial by grouping:

[tex]P(x)=x^2(x-4)+1(x-4)[/tex]

We factor further to obtain:

[tex]P(x)=(x^2+1)(x-4)[/tex]

[tex]P(x)=(x^2-\sqrt{-1}^2)(x-4)[/tex]

We apply difference of two squares to get:

[tex]P(x)=(x-i)(x+i)(x-4)[/tex]

Answer:

(x+1)(x-1)(x+4)

Step-by-step explanation:

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