Factor x^3 – 6x^2 + 5x + 12 ?

1 Answer
Feb 23, 2018

=> (x+1)(x-3)(x-4)

Factors are x = -1, 3, 4

Explanation:

(x^3 -6x^2 + 5x + 12)

Since the sum of the coefficients of the terms is zero, x +1 is a factor.

Using synthetic division,

color(white)(aaa) -1 color(white)(aaa)|color(white)(aaa)1color(white)(aaa)-6color(white)(aaa)5color(white)(aaa)12

color(white)(aaaaaaaaa)|color(white)(aaa)darrcolor(white)(aa)-1color(white)(aaa)7color(white)(a)-12

color(white)(aaaaaaaaa)|………………………

color(white)(aaaaaaaaaaaaaa)1color(white)(aaa)-7color(white)(aaa)12color(white)(aaa)0

=> (x+1) (x^2 - 7x + 12)

=> (x+1)(x^2 - 3x - 4x + 12)

=> (x + 1) (x(x - 3) -4 (x-3))

=> (x+1)(x-3)(x-4)

Factors are x = -1, 3, 4