# How do you factor # x^3-3x^2+6x-18#?

##### 1 Answer

Sep 3, 2016

#### Explanation:

Notice that the ratio between the first and second terms is the same as that between the third and fourth terms, so this will factor by grouping:

#x^3-3x^2+6x-18 = (x^3-3x^2)+(6x-18)#

#color(white)(x^3-3x^2+6x-18) = x^2(x-3)+6(x-3)#

#color(white)(x^3-3x^2+6x-18) = (x^2+6)(x-3)#

That's as far as you can go using Real coefficients since

#color(white)(x^3-3x^2+6x-18) = (x^2-(sqrt(6)i)^2)(x-3)#

#color(white)(x^3-3x^2+6x-18) = (x-sqrt(6)i)(x+sqrt(6)i)(x-3)#