Let K be one of Q, R, C (or any field). Prove that a polynomial f(x) in K[x] of degree 3 is reducible if and only if f(x) has a root in K.
I need help on the backward proof. I mean "If f has a root, then f is reducible".
Please

Question

Let K be one of Q, R, C (or any field). Prove that a polynomial f(x) in K[x] of degree 3 is reducible if and only if f(x) has a root in K.
I need help on the backward proof. I mean "If f has a root, then f is reducible". 
Please

loser66 · Answer

I got the forward one. "if f is reducible, f has a root."

loser66 · Answer

attachment

ganeshie8 · Answer

Is it like, if f has a root, then it can be expressed as a product of two factors ?

loser66 · Answer

Yes, I think so

loser66 · Answer

not just 2, can be 3

ganeshie8 · Answer

i wont be useful here

loser66 · Answer

Thanks anyway. It's better than no one come. :)

ganeshie8 · Answer

hope somebody assists sooner, good luck! @SithsAndGiggles

loser66 · Answer

@kirbykirby

loser66 · Answer

oh, nvm, I got it. hihihi
If $\alpha $ is a root of f then $(x-\alpha) |f(x)$ ) or f(x) = \((x-\alpha) *q(x)
That shows f(x) is reducible