I have this shit to factorize. X^3+x^2-4x-x. Now if its -5 there

> X^3+x^2-4x-x

No offense, but are you seriously sure that it's not a typo?

>>375296
It's probably a typo, but here you go:
x^2 + x - 5 =
x^2 + x + 0.25 - 5.25 =
(x + 0.5)^2 - 5.25 = 0 iff
(x + 0.5)^2 = 5.25
x + 0.5 = +-sqrt(5.25)
x = -0.5 +- sqrt(5.25)

so the factorization is
x(x - (-0.5 + sqrt(5.25)))(x - (-0.5 - sqrt(5.25)))

>>375334

You took the latter equation instead of the former one and have forgotten the one x before the round bracket. ;)

>>375296
Assuming that it is
x^3 + x^2 - 4x - 4
= (x + 1)(x^2 - 4)
= (x + 1)(x + 2)(x - 2)

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87KB, 837x879px

>>375296
I didnt fanthom the idea of it being a type. Thanks mates

Assuming it wasn't a typo

let y = x^3 + x^2 - 4x -x

y = x^3 + x^2 - 5x
y = x (x^2 + x -5)


let z = x^2 + x - 5

completing the square

consider
(x+ 1/2)^2 = x^2 + x +1/4

so

(x+ 1/2)^2 - 1/4 = x^2 + x

let w = (x+ 1/2)^2 - 1/4 = x^2 + x

therefore z = w - 5

z = (x+ 1/2)^2 - 1/4 - 5

z = (x+ 1/2)^2 - 5.25

finding the roots where z = 0

0 = (x+ 1/2)^2 - 5.25

(x+ 1/2)^2 = 5.25

x = -1/2 +- (5.25^0.5)

Which gives two answers
-1/2 + (5.25^0.5)
-1/2 - (5.25^0.5)

So

y = x (x - (-1/2 + (5.25^0.5)))(x - (-1/2 - (5.25^0.5)))