Question

how can i factor this out completly

x^4+x^3-12


i know that4*-3=-12 but how can i get that middle term

x^2*x^2=x^4

first you cannot take out any GCF.
so if you decide to use grouping, you can create an equivalent problem:
x^4 + x^3 - 6 - 6
then by using grouping (the x-terms and the integers):
x^3 ( x + 1) - 6(1+1)
simplified, that is:
(x^3 - 6) - (x + 3) [combining the parentheses)
you can now simply factor out the x-cubed binomial with less difficulty.

as you could *probably* see, you cannot factor this, so using the quadratic formula:

x^3 + 0x -6
a = 1
b = 0
c = -6

-b +/- sqrt(b^2 - 4ac) / 2a

0 +/- sqrt(0 - 24) / 2

(since sqrt(-24) doesn't exist, you have to use i)

0 +/- 2 x 6i / 2

a) 0 + 2 x 6i / 2
12 i / 2
6 i

b) 0 -2 x 6i / 2
-12 i / 2
-6 i

so x could equal 6i or -6i

Sorry if this was tedious, but it wasn't easy. hope you understand.