f(x)= x^4 -x^3 + 7x^2 - 9x -18

First we will rearrange terms.

==> (x^4 + 7x^2 -18) - x^3 9x = 0

Now we will factor :

==> (x^2 +9)(x^2-2) - x(x^2+9)= 0

Now we will factor (x^2+9) from both terms:

==> (x^2+9)(x^2-2-x)= 0

==> (x^2+9)(x^2-x-2)= 0

==> (x^2+9)(x-2)(x+1)...

## Unlock

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

f(x)= x^4 -x^3 + 7x^2 - 9x -18

First we will rearrange terms.

==> (x^4 + 7x^2 -18) - x^3 9x = 0

Now we will factor :

==> (x^2 +9)(x^2-2) - x(x^2+9)= 0

Now we will factor (x^2+9) from both terms:

==> (x^2+9)(x^2-2-x)= 0

==> (x^2+9)(x^2-x-2)= 0

==> (x^2+9)(x-2)(x+1) = 0

==> x1= 2

==> x2= -1

==> x3= 3i

==> x4= -3i

==> Then we have two real roots {2, -1} and two complex roots { 3i, -3i}

==> x= { -1, 2, -3i, 3i}