Question: Let F[7]=Z[7 ]be the finite field with 7 elements and m=x(x+1)(x+6)=x^(3)+6 x in F[7][x].

> 1) letJ subset F[7][x] be the set of all polynomials h in F[7][x] sloving the interpolation problem h(0);
=1,h(1)=5,h(6)=2. computer the unique polynomial f∈J of least degree.

2) find a surjective ring homomorphism ×:F[7][x]->F[7]^(3) such that Ker×=={rm:r∈F[7][x]};and computer ×(f)and×(x^2+3*x+2).

3) show thatJ=f+Ker×={f+rm:r∈ F[7][x]}.

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