Question

If $f\left(x\right)\ne 0_f$and $f\left(x\right)$is relatively prime to $0_f$, what can be said about $f\left(x\right)$?

Short answer

$f\left(x\right)$is a non-zero constant polynomial.

Step-by-step solution

Determine what can be said about f(x)

With any non-zero polynomials,$f\left(x\right)\in F\left[x\right]$ having a leading coefficient $a_n$, it is obtained that $\left(f\left(x\right),0={a_n}^{-1}f\left(x\right)\right)$. When $f\left(x\right)$is relatively prime to 0 then,${a_n}^{-1}f\left(x\right)=1$ , t

 Step 2: Conclusion

As a result,$h\left(x\right)={a_0}^{-1}d\left(x\right)$. This case is true only when f(x) is a non-zero constant polynomial.

Hence, f(x) is a non-zero constant polynomial.