Question

Phân tích đa thức sau thành nhân tử: n⁴+2n³+3n²​+2n+1

Answer 1

\(=\left(n^4+n^3+n^2\right)+\left(n^3+n^2+n\right)+\left(n^2+n+1\right)\)

\(=n^2\left(n^2+n+1\right)+n\left(n^2+n+1\right)+\left(n^2+n+1\right)\)

\(=\left(n^2+n+1\right)\left(n^2+n+1\right)\)

\(=\left(n^2+n+1\right)^2\)

Answer 2

n⁴ + 2n³ + 3n² + 2n + 1

= n⁴ + n³ + n² + n³ + n² + n + n² + n + 1

= n²(n² + n +1) + n(n² + n +1) + (n² + n + 1)

= (n² + n +1)(n² + n +1)

= (n² + n +1)²