Câu hỏi của Nguyễn Lê Minh Thy

Question

phân tích đa thức thành nhân tử$x^3+2x^2+2x+1$$x^3-4x^2+12x-27$$x^4+2x^3+2x^2+2x+1$$x^4-2x^3+2x-1$

Dương Lam Hàng · Accepted Answer

$x^3+2x^2+2x+1=\left(x^3+1\right)+\left(2x^2+2x\right)$$=\left(x+1\right)\left(x^2-x+1\right)+2x\left(x+1\right)$$=\left(x+1\right)\left(x^2-x+1+2x\right)=\left(x+1\right)\left(x^2+x+1\right)$$x^3-4x^2+12x-27=x^3-3x^2-x^2+3x+9x-27$$=x^2\left(x-3\right)-x\left(x-3\right)+9\left(x-3\right)$$=\left(x-3\right)\left(x^2-x+9\right)$$x^4+2x^3+2x^2+2x+1=x^4+x^2+2x^3+x^2+2x+1$$=x^2\left(x^2+1\right)+2x\left(x^2+1\right)+\left(x^2+1\right)$$=\left(x^2+1\right)\left(x^2+2x+1\right)$$=\left(x^2+1\right)\left(x+1\right)^2$$x^4-2x^3+2x-1=\left(x^4-1\right)-2x\left(x^2-1\right)$$=\left(x^2-1\right)\left(x^2+1\right)-2x\left(x^2-1\right)$$=\left(x^2-1\right)\left(x^2+1-2x\right)=\left(x^2-1\right)\left(x-1\right)^2$Câu trả lời: $x^3+2x^2+2x+1=\left(x^3+1\right)+\left(2x^2+2x\right)$$=\left(x+1\right)\left(x^2-x+1\right)+2x\left(x+1\right)$$=\left(x+1\right)\left(x^2-x+1+2x\right)=\left(x+1\right)\left(x^2+x+1\right)$$x^3-4x^2+12x-27=x^3-3x^2-x^2+3x+9x-27$$=x^2\left(x-3\right)-x\left(x-3\right)+9\left(x-3\right)$$=\left(x-3\right)\left(x^2-x+9\right)$$x^4+2x^3+2x^2+2x+1=x^4+x^2+2x^3+x^2+2x+1$$=x^2\left(x^2+1\right)+2x\left(x^2+1\right)+\left(x^2+1\right)$$=\left(x^2+1\right)\left(x^2+2x+1\right)$$=\left(x^2+1\right)\left(x+1\right)^2$$x^4-2x^3+2x-1=\left(x^4-1\right)-2x\left(x^2-1\right)$$=\left(x^2-1\right)\left(x^2+1\right)-2x\left(x^2-1\right)$$=\left(x^2-1\right)\left(x^2+1-2x\right)=\left(x^2-1\right)\left(x-1\right)^2$

kudo shinichi · Answer

$x^3+2x^2+2x+1=\left(x^3+x^2\right)+\left(x^2+x\right)+\left(x+1\right)$                                    $=x^2.\left(x+1\right)+x.\left(x+1\right)+\left(x+1\right)$                                   $=\left(x+1\right).\left(x^2+x+1\right)$$x^3-4x^2+12x-27$$=\left(x^3-x^2\right)-\left(3x^2-3x\right)+\left(9x-27\right)$$=x^2.\left(x-1\right)-3x.\left(x-1\right)+9.\left(x-3\right)$$=\left(x-1\right).\left(x^2-3x\right)+9.\left(x-3\right)$$=x.\left(x-1\right).\left(x-3\right)+9.\left(x-3\right)$$=\left(x-3\right)\left[x.\left(x-1\right)+9\right]$Câu trả lời: $x^3+2x^2+2x+1=\left(x^3+x^2\right)+\left(x^2+x\right)+\left(x+1\right)$                                    $=x^2.\left(x+1\right)+x.\left(x+1\right)+\left(x+1\right)$                                   $=\left(x+1\right).\left(x^2+x+1\right)$$x^3-4x^2+12x-27$$=\left(x^3-x^2\right)-\left(3x^2-3x\right)+\left(9x-27\right)$$=x^2.\left(x-1\right)-3x.\left(x-1\right)+9.\left(x-3\right)$$=\left(x-1\right).\left(x^2-3x\right)+9.\left(x-3\right)$$=x.\left(x-1\right).\left(x-3\right)+9.\left(x-3\right)$$=\left(x-3\right)\left[x.\left(x-1\right)+9\right]$

Đường Quỳnh Giang · Answer

$x^3+2x^2+2x+1$$=\left(x^3+1\right)+\left(2x^2+2x\right)$$=\left(x+1\right)\left(x^2-x+1\right)+2x\left(x+1\right)$$=\left(x+1\right)\left(x^2+x+1\right)$Câu trả lời: $x^3+2x^2+2x+1$$=\left(x^3+1\right)+\left(2x^2+2x\right)$$=\left(x+1\right)\left(x^2-x+1\right)+2x\left(x+1\right)$$=\left(x+1\right)\left(x^2+x+1\right)$

Khoá học trên OLM (olm.vn)

Khoá học trên OLM (olm.vn)