prove linear independence of polynomials Let $f_1,...,f_k$ be polynomials at field $K$ not including the zero polynomial and $\deg f_i \neq \deg f_j$ for every $i \neq j$ Show that polynomials $f_1,...,f_k $ are linear independent. 
I don't know how to use the information that $\deg f_i \neq \deg f_j$. 
I will try to consider a linear combination $a_1f_1+...+a_kf_k=0$ and show that then $a_1=...=a_k=0$ but I don't know how do derive it. 

Suppose that  $f_1 ,f_2 ,...,f_k$ are linear dependent and let $f_j $ be the polynomial whose degree is the largest then $f_j = c_1f_1+ ...c_{j-1}f_{j-1} + c_{j+1}f_{j+1}+.... +c_{k}f_{k}$ but the degree of right hand side is less thar left hand side and this is contradiction 
