err how do i factor this?

Question

x^4 - 6x³ + 17x² -54x + 72

= ?

(x+3) (x-2) .. err nvm

help !!~!!! >< thank you~!

Answer 1

f (x) = x^4 - 6x³ + 17 x² - 54x + 72
f(2) = 16 - 48 + 68 - 108 + 72
f(2) = 0
Thus x - 2 is a factor.
To find other factors, divide by x - 2 using synthetic division:-

2|1___-6___17___-54___72
|_____2___-8____18__-72
|1___-4____9____-36__0

f(x) = (x - 2)(x³ - 4x² + 9x - 36)
g(x) = x³ - 4x² + 9x - 36
g(4) = 64 - 64 + 36 - 36 = 0
Thus x - 4 is a factor of g(x)

4|1___-4___9___-36
|_____4___0____36
|1____0___9____0

x - 4 is a factor of g(x)

f(x) = (x - 3)(x - 4)(x² + 9)

Answer 2

Basically, trial and error. There is no quick way to go about it.

I got (x^2-6x+8)*(x^2+9) which simplifies further to
(x-2)(x-4)(x^2+9)

Answer 3

(x²+9)(x-2)(x-4)