# Homework Help: Simplifying a ?quad?nomial

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

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