Question

Factor x^2 -3x-3 in F5(x) p=5

it says -3 =2(mod5)-----------how did they come up with this
x^2-3x-3 = x^2 -3x +2--------how did they come up with this

Answer 1

`-3=2-5\implies -3\mod5=2\mod5`

When taking a polynomial modulo
`n`, you reduce its terms' coefficients modulo
`n`, so that, in conjunction with the result above,


`x^2-3x-3\equiv x^2-3x+2\mod5`

For completeness, the linear term's coefficient should also get reduced in the same way as the constant term, so that


`x^2-3x-3\equiv x^2+2x+2\mod5`