(x^3+x+1)(x^3+x)−2 phân tích đa thức thành nhân tử

slick back

$\left(x^3+x+1\right)\left(x^3+x\right)-2$

$=\left(x^3+x\right)^2+\left(x^3+x\right)-2$

$=\left(x^3+x\right)^2-\left(x^3+x\right)+2\left(x^3+x\right)-2$

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

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

$=\left(x^3+x-1\right)\left\lbrack\left(x^3-x^2+2x\right)+\left(x^2-x+2\right)\right\rbrack$

$=\left(x^3+x-1\right)\left\lbrack x\left(x^2-x+2\right)+\left(x^2-x+2\right)\right\rbrack$

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