Question

Phân tích đa thức thành nhân tử
\(1,x^{11}+x^{\text{4}}+1\)

\(2,x^{11}+x^7+1\)

giúp mk vs mk đag cần gấp

Answer 1

x¹¹+x⁴+1

= x¹¹+x¹⁰+x⁹-x¹⁰-x⁹-x⁸+x⁸+x⁷+x⁶-x⁷-x⁶-x⁵+x⁵+x⁴+x³-x³-x²-x+x²+x+1

= x⁹(x²+x+1)-x⁸(x²+x+1)+x⁶(x²+x+1)-x⁵(x²+x+1)+x³(x²+x+1)-x(x²+x+1)+(x²+x+1)

= (x²+x+1)(x⁹-x⁸+x⁶-x⁵+x³-x+1)

Answer 2

x¹¹+x⁷+1

= x¹¹+x¹⁰+x⁹-x¹⁰-x⁹-x⁸+x⁸+x⁷+x⁶-x⁶-x⁵-x⁴+x⁵+x⁴+x³-x³-x²-x+x²+x+1

= x⁹(x²+x+1)-x⁸(x²+x+1)+x⁶(x²+x+1)-x⁴(x²+x+1)+x³(x²+x+1)-x(x²+x+1)+(x²+x+1)

= (x²+x+1)(x⁹-x⁸+x⁶-x⁴+x³-x+1)