Question

Phân tích đa thức thành nhan tử x⁴ + 1997x² + 1996x + 1997

Answer 1

=(x⁴+x²+1)+(1996x²+1996x+1996)

=(x²+x+1)(x²-x+1)+1996(x²+x+1)

=(x²+x+1)(x²-x+1+1996)

Answer 2

\(x^4+1997x^{ 2}+1996x+1997\)

\(=\left(x^4-x\right)+\left(1997x^2+1997x+1997\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+1997\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left[x\left(x-1\right)+1997\right]\)

\(=\left(x^2+x+1\right)\left(x^2-x+1997\right)\)