Answer:
[tex]f(x)=(x^2+3)(x-2)[/tex]
Step-by-step explanation:
so [tex]f(x)= x^3-2x^2+3x-6\\[/tex]
In order to factor this we try to factor it based on the order so:
[tex]x^3-2x^2+3x-6[/tex]
If you look at this equation we can see that the first two terms are factorable:
[tex]x^3-2x^2=\\x^2(x-2)[/tex]
And the last two terms are also factorable:
[tex]3x-6=\\3(x-2)[/tex]
Combining them together we get:
[tex]f(x)=x^2(x-2)+3(x-2)[/tex]
We can see that in these terms (x-2) is common so we can rewrite this as:
[tex]f(x)=(x^2+3)(x-2)[/tex]
