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)
