Câu hỏi của Tú Thanh Hà

Question

Phân tích đa thức thành nhân tử:

$a,x^3+x^2+4$

$b,-x^3-6x^2-6x+1$

$c,2x^3-3x^2+3x-1$

$d,3x^3-14x^2+4x+3$

$e,x^4+2x^3+x^2+x+1$

GIÚP MÌNH NHANH NHÉ :)

Ťɧε⚡₣lαsɧ · Accepted Answer

d) $3x^3-14x^2+4x+3=3x^3+x^2-15x^2-5x+9x+3$

$=x^2\left(3x+1\right)-5x\left(3x+1\right)+3\left(3x+1\right)$

$=\left(x^2-5x+3\right)\left(3x+1\right)$

e) $x^4+2x^3+x^2+x+1=x^4+x^3+x^3+x^2+x+1$

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

$=\left(x^3+x^2+1\right)\left(x+1\right)$Câu trả lời: d) $3x^3-14x^2+4x+3=3x^3+x^2-15x^2-5x+9x+3$

$=x^2\left(3x+1\right)-5x\left(3x+1\right)+3\left(3x+1\right)$

$=\left(x^2-5x+3\right)\left(3x+1\right)$

e) $x^4+2x^3+x^2+x+1=x^4+x^3+x^3+x^2+x+1$

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

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

Ťɧε⚡₣lαsɧ · Answer

a) $x^3+x^2+4=x^3+2x^2-x^2-4$

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

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

c) $2x^3-3x^2+3x-1=2x^3-x^2-2x^2+x+2x-1$

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

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

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

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

c) $2x^3-3x^2+3x-1=2x^3-x^2-2x^2+x+2x-1$

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

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

Bài 9: Phân tích đa thức thành nhân tử bằng cách phối hợp nhiều phương pháp