Câu hỏi của Linh An Trần

Question

(x2+x+1)(x2+x+2-12)

(x2+x)2-2(x2+x)-15

(x2+2x)2+9x2+18x+20

(x2+3x+1)(x2+3x+2)-6

phân tích dùm nha

Nguyễn Nam · Accepted Answer

b) $\left(x^2+x\right)^2-2\left(x^2+x\right)-15$

$=\left(x^2+x\right)^2-2\left(x^2+x\right)+1-16$

$=\left[\left(x^2+x\right)^2-2\left(x^2+x\right).1+1^2\right]-16$

$=\left(x^2+x-1\right)^2-4^2$

$=\left(x^2+x-1-4\right)\left(x^2+x-1+4\right)$

$=\left(x^2+x-5\right)\left(x^2+x+3\right)$Câu trả lời: b) $\left(x^2+x\right)^2-2\left(x^2+x\right)-15$

$=\left(x^2+x\right)^2-2\left(x^2+x\right)+1-16$

$=\left[\left(x^2+x\right)^2-2\left(x^2+x\right).1+1^2\right]-16$

$=\left(x^2+x-1\right)^2-4^2$

$=\left(x^2+x-1-4\right)\left(x^2+x-1+4\right)$

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

Nguyễn Nam · Answer

a) $\left(x^2+x+1\right)\left(x^2+x+2\right)-12$

$=\left(x^2+x+1\right)\left[\left(x^2+x+1\right)+1\right]-12$

$=\left(x^2+x+1\right)^2+\left(x^2+x+1\right)-12$

$=\left(x^2+x+1\right)^2+4\left(x^2+x+1\right)-3\left(x^2+x+1\right)-12$

$=\left[\left(x^2+x+1\right)^2+4\left(x^2+x+1\right)\right]-\left[3\left(x^2+x+1\right)+12\right]$

$=\left(x^2+x+1\right)\left[\left(x^2+x+1\right)+4\right]-3\left[\left(x^2+x+1\right)+4\right]$

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

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

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

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

$=\left(x^2+x+5\right)\left[\left(x^2-x\right)+\left(2x-2\right)\right]$

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

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

c) $\left(x^2+2x\right)^2+9x^2+18x+20$

$=\left(x^2+2x\right)^2+9\left(x^2+2x\right)+20$

$=\left(x^2+2x\right)^2+4\left(x^2+2x\right)+5\left(x^2+2x\right)+20$

$=\left[\left(x^2+2x\right)^2+4\left(x^2+2x\right)\right]+\left[5\left(x^2+2x\right)+20\right]$

$=\left(x^2+2x\right)\left[\left(x^2+2x\right)+4\right]+5\left[\left(x^2+2x\right)+4\right]$

$=\left[\left(x^2+2x\right)+4\right]\left[\left(x^2+2x\right)+5\right]$

$=\left(x^2+2x+4\right)\left(x^2+2x+5\right)$

d) $\left(x^2+3x+1\right)\left(x^2+3x+2\right)-6$

$=\left(x^2+3x+1\right)\left[\left(x^2+3x+1\right)+1\right]-6$

$=\left(x^2+3x+1\right)^2+\left(x^2+3x+1\right)-6$

$=\left(x^2+3x+1\right)^2-2\left(x^2+3x+1\right)+3\left(x^2+3x+1\right)-6$

$=\left[\left(x^2+3x+1\right)^2-2\left(x^2+3x+1\right)\right]+\left[3\left(x^2+3x+1\right)-6\right]$

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

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

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

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