lovensdibre
lovensdibre lovensdibre
  • 01-09-2017
  • Mathematics
contestada

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

Respuesta :

lisboa lisboa
  • 23-12-2018

Answer:

(x-3)(x+i)(x-i)

Step-by-step explanation:

[tex]x^3-3x^2+x-3[/tex]

We apply grouping method

We group first two terms and last two terms

[tex](x^3-3x^2)+(x-3)[/tex]

Take out GCF x^2 from first group. Also take out 1 from second group

[tex]x^2(x-3)+1(x-3)[/tex]

[tex](x-3) (x^2+1)[/tex]

Now we factor x^2 + 1

We  use difference of square formula

a^2 - b^2 = (a+b)(a-b)

x^1 + 1 can be written as [tex]x^2 - (-1)[/tex], the value of -1 is i^2

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

x^2 - i^2 = (x+i)(x-i)

Final answer is (x-3)(x+i)(x-i)

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