# How do you factor #f(x)=x^3+3x^2-12x-18#?

##### 1 Answer

#### Answer:

#### Explanation:

To factorize a n-degree-polynomial function, one must discover its roots that will allow to rearrange the function in this way

For a polynomial of the third degree, when all coefficients are real numbers, there's at least one real root. The other two roots are either real numbers or complex conjugate numbers.

For a general solution of roots of the third degree, requiring some ability to work with complex numbers, I recommend this source:

Roots of a cubic function

But we can try to resolve the problem in the easy way.

The coefficient d may help us to find at least one real root.

This is why we should try the numbers 1, 2, 3, 6, 9, 18 and 1/2, 1/3, 1/6, 1/9 and 1/18 to verify if at least one of them is a root of the function.

In the present case, we discover that 3 is a root (

Then we should divide the polynomial by

*_**_**_*_

*_**_**_ #"
"x^2+6x+6#
#" "6x^2-12x#
#" "-6x^2+18x#
#" "# *

*_*

*_*

#" "6x-18#

#" "-6x+18#

#" "#

*_***___**

*_*The second degree factor can still be further factorized:

Then the function factorized is