Question

Phân tích đa thức sau thành thân tử:

x⁴+6x³+11x²+6x+1

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Answer 1

\(x^4+6x^3+11x^2+6x+1\)

\(=x^4+6x^3+9x^2+2x^2+6x+1\)

\(=x^4+9x^2+1+6x^3+2x^2+6x\)

\(=x^4+9x^3+1^2+2x.3x+2x^2+2.3\)

\(=\left(x^2+3x+1\right)^2\)

Answer 2

x^4+6x^3+11x^2+6x+1
= x^4 + 6x^3 + 9x² + 2x² + 6x + 1
= x^4 + 9x² + 1 + 6x^3 + 2x² + 6x
= x^4 + 9x² + 1² + 2.x².3x + 2.x².1 + 2.3x.1
= (x² + 3x + 1)²