Question

Phân tích đa thức thành nhân tử : x⁴ + x³ + 3x² +2x + 2

Answer 1

Lời giải:

Ta có:

\(x^4+x^3+3x^2+2x+2\)

\(=x^4-x+x^3-1+3x^2+3x+3\)

\(=x(x^3-1)+(x^3-1)+3(x^2+x+1)\)

\(=(x^3-1)(x+1)+3(x^2+x+1)\)

\(=(x-1)(x^2+x+1)(x+1)+3(x^2+x+1)\)

\(=(x^2+x+1)(x^2-1)+3(x^2+x+1)\)

\(=(x^2+x+1)(x^2-1+3)=(x^2+x+1)(x^2+2)\)

Answer 2

Cách khác :

\(x^4+x^3+3x^2+2x+2\)

\(=\left(x^4+x^3+x^2\right)+\left(2x^2+2x+2\right)\)

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

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