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.
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