a)\(-6x^3+18^2+60x\)
\(=6x.-x^2+6x.3x+6x.10\)
=\(6x\left(-x^2+3x+10\right)\)
b)\(x^7+x^2+1\)
=\(\left(x^7-x\right)+\left(x^2+x+1\right)\)
=\(x\left(x^6-1\right)+\left(x^2+x+1\right)\)
\(=x\left(x^3-1\right).\left(x^3+1\right)+\left(x^2+x+1\right)\)
=\(x\left(x-1\right).\left(x^2+x+1\right).\left(x^3+1\right)+\left(x^2+x+1\right)\)
=\(\left(x^2+x+1\right).\left[x.\left(x-1\right).\left(x^3+1\right)+1\right]\)
\(=\left(x^2+x+1\right).\left[\left(x^2-x\right).\left(x^3+1\right)+1\right]\)
\(=\left(x^2+x+1\right).\left(x^5+x^4+x^2-x+1\right)\)
Bạn học tốt nhé!
c)\(x^{10}+x^5+1\)
\(=x^{10}+x^9-x^9+x^8-x^8+x^7-x^7+x^6-x^6+\)\(x^5+x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x-x+1\)
=\(\left(x^{10}+x^9+x^8\right)-\left(x^9+x^8+x^7\right)+\left(x^7+x^6+x^5\right)\)
\(-\left(x^6+x^5+x^4\right)+\left(x^5+x^4+x^3\right)-\left(x^3+x^2+x\right)\)
\(+\left(x^2+x+1\right)\)
=\(x^8\left(x^2+x+1\right)-x^7\left(x^2+x+1\right)+x^5\left(x^2+x+1\right)\)\(-x^4\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x\left(x^2+x+1\right)\)
\(+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right).\left(x^8-x^7+x^5-x^4+x^3-x+1\right)\)
Lộn xộn quá ha, chúc bạn học thật giỏi!
