how do we write $f(x)=x^{4}-x^{3}+14x^{2}+5x+16$ over $F\_{3}$?
 answer given is:over $F\_{3}:x^{4}-x^{3}+14x^{2}+5x+16=x^{4}-x^{3}-x^{2}-x+1$

how do we get this?

similarly...over $F\_{7}=x^{4}-x^{3}+14x^{2}+5x+16=x^{4}-x^{3}-2x+2$

how do we get it?