Răspuns :
x⁴+2x³+2x+1
x⁴+x³+x³+x²+x²+x²+x+x+1
x²×(x²+x+1)+x×(x²+x+1)+x²+x+1
(x²+x+1)×(x²+x+1)
(x²+x+1)²
Explicație pas cu pas:
x⁴+2x³+3x²+2x+1 =
x²(x²+x+1)+x(x²+x+1)+x²+x+1=
(x²+x+1)²
x⁴+2x³+2x+1
x⁴+x³+x³+x²+x²+x²+x+x+1
x²×(x²+x+1)+x×(x²+x+1)+x²+x+1
(x²+x+1)×(x²+x+1)
(x²+x+1)²
Explicație pas cu pas:
x⁴+2x³+3x²+2x+1 =
x²(x²+x+1)+x(x²+x+1)+x²+x+1=
(x²+x+1)²