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)
