is this factorable?

[spacewater]

problem
find the zeros algebraically
$\displaystyle f(x) = 3x^2-12x+3$

steps
$\displaystyle f(x)= 3(x^2-4x+1)$

this is farthest i got. How can I factor this problem?

 

[Deleted member 4993]

problem
find the zeros algebraically
$\displaystyle f(x) = 3x^2-12x+3$

steps
$\displaystyle f(x)= 3(x^2-4x+1)$ ? This function has real but irrational roots. That means this function can be factored - but not with "nice" rational numbers.

this is farthest i got. How can I factor this problem?

 

[pka]

problem
find the zeros algebraically
$\displaystyle f(x) = 3x^2-12x+3$
steps
$\displaystyle f(x)= 3(x^2-4x+1)$

It is not too bad.
$\displaystyle 3(x^4-4x+1)=3(x-2-\sqrt{3})(x-2+\sqrt{3})$

 

[stapel]

find the zeros algebraically
$\displaystyle f(x) = 3x^2-12x+3$

How can I factor this problem?

Do the instructions specify that you must factor to find the zeroes? Or are you allowed to use the Quadratic Formula instead? :?: