Find the sum and product of $f(x)=3x-5, g(x)=2x^2-4x+3$ in $Z_8$. Find the sum and product of $f(x)=3x-5, g(x)=2x^2-4x+3$ in $Z_8$.

Does using high school style of solving this yields a different answer? 

What would be the answer?
$f(x) + g(x) = 3x-5 + 2x^2-4x+3 = 2x^2-x-2=2x^2+7x+6(\mod 8)$

$f(x) \times  g(x) = (3x-5) \times (2x^2-4x+3) \\= 6x^3-12x^2+9x-10x^2+20x-15 \\= 6x^3-22x^2+29x -15 \\= 6x^3+2x^2+5x +1 (\mod 8)$
$f(x) + g(x) = 3x-5 + 2x^2-4x+3 = 2x^2-x-2=2x^2+7x+6(\mod 8)$

$f(x) \times  g(x) = (3x-5) \times (2x^2-4x+3) \\= 6x^3-12x^2+9x-10x^2+20x-15 \\= 6x^3-22x^2+29x -15 \\= 6x^3+2x^2+5x +1 (\mod 8)$