Question

Factor the polynomial function over the complex numbers.

f(x)=x^3−2x^2+3x−6

Enter your answer in the box.

Answer 1

`f(x)=(x^2+3)(x-2)`

Explanation:

so
`f(x)= x^3-2x^2+3x-6\\`

In order to factor this we try to factor it based on the order so:

`x^3-2x^2+3x-6`

If you look at this equation we can see that the first two terms are factorable:

`x^3-2x^2=\\x^2(x-2)`

And the last two terms are also factorable:

`3x-6=\\3(x-2)`

Combining them together we get:

`f(x)=x^2(x-2)+3(x-2)`

We can see that in these terms (x-2) is common so we can rewrite this as:

`f(x)=(x^2+3)(x-2)`