1. Apr 18, 2012

Patdon10

1. The problem statement, all variables and given/known data

simplify -x^3 - 3x^2 - 4x - 2
It is equal to -(x-1)(x^2 + 2x + 2)

Not sure how to get that answer, nor how to start it.

2. Apr 19, 2012

Mentallic

The word you're looking for is to factorize it, not simplify it. You can't simplify it in the sense that you can simply $$\frac{\sin(x)}{\cos(x)}$$ to become $$\tan(x)$$ for example.

Ok so first of all, in order to factorize that cubic you'll need to know one of its roots. Do you know how to check if a polynomial has rational roots?

3. Apr 19, 2012

HallsofIvy

Staff Emeritus
Good! Because you shouldn't get that "answer". It is wrong.

Setting x= 1 in that polynomial gives -(1)- 3(1)- 4(1)- 2= -(1+3+ 4+ 2)= -10, not 0. Since x= 1 does NOT make that polynomial 0, x- 1 is NOT a factor. -x^3- 3x^2- 4x- 2 is NOT equal to -(x- 1)(x^2+ 2x+ 2).

However, setting x= -1 gives -(-1)- 3(1)- 4(-1)- 2= 1- 3+ 4- 2= 0 so x-(-1)= x+ 1 is a factor. Divide -x^3- 3x^2- 4x- 2 by x+1 to get the other factor.

4. Apr 19, 2012

Mentallic

Ah yes I shouldn't noticed that at quick glance since $$-x^3 - 3x^2 - 4x - 2 = -(x^3+3x^2+4x+2)$$ which should have all same sign coefficients in its factors

5. Apr 19, 2012

SammyS

Staff Emeritus
-(x-1)(x^2 + 2x + 2)

is equivalent to:

-x^3 -x^2 + 2