Question

Көбейткіштерге жіктеу 5.143

Answer 1

$1)\; \; x^8+x^4+1=(x^8+2x^4+1)-x^4=(x^4+1)^2-(x^2)^2=\\\\=(x^4+1-x^2)(x^4+1+x^2)=\Big (x^4-x^2+1\Big )\Big (((x^2)^2+2x^2+1)-x^2\Big )=\\\\=\Big (x^4-x^2+1\Big )\Big ((x^2+1)^2-x^2\Big )=(x^4-x^2+1)(x^2+1-x)(x^2+1+x)=\\\\=(x^4-x^2+1)(x^2-x+1)(x^2+x+1)\\\\2)\; \; x^4+x^2y^2+y^4=(x^4+2x^2y^2+y^4)-x^2y^2=(x^2+y^2)^2-(xy)^2=\\\\=(x^2+y^2-xy)(x^2+y^2+xy)\\\\3)\; \; a^3-3a+2=(a-1)(a^2+a-2)=(a-1)(a+2)(a-1)=\\\\=(a-1)^2(a+2)\\\\4)\; \; x^3+3x^2-4=(x-1)(x^2+4x+4)=(x-1)(x+2)^2$