Question

x+x^2+x^3+x^4+x^5+…+x^13+x^14x+^15 phân tích đa thức thành nhân tử theo cách nâng cao

Answer 1

Ta có: \(x+x^2+x^3+x^4+x^5+x^6+\cdots+x^{13}+x^{14}+x^{15}\)

\(=\left(x+x^2+x^3\right)+\left(x^4+x^5+x^6\right)+\cdots+\left(x^{13}+x^{14}+x^{15}\right)\)

\(=x\left(1+x+x^2\right)+x^4\left(1+x+x^2\right)+\cdots+x^{13}\left(1+x+x^2\right)\)

\(=\left(x^2+x+1\right)\left(x+x^4+\cdots+x^{13}\right)\)

\(=x\left(x^2+x+1\right)\left(1+x^3+x^6+x^9+x^{12}\right)\)

Answer 2

x(1+x*1+...+x*14)