Question

Calculate (2x+3)(3x+4) in Z5[x]:

Answer 1

Open brackets in (2x+3)(3x+4)=6x²+8x+9x+12=6x²+17x+12. Express coefficients in this expression via multiples of 5 and remainders: 6=5*1+1, 17=5*3+2, 12=5*2+2. The given expression in Z5[x] turns into x²+2x+2. Answer: x²+2x+2.