BC
3
K
Khách
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LM
2
KT
3 tháng 8 2018
a) \(x^4+4=x^4+4x^2+4-4x^2=\left(x^2+2\right)^2-4x^2=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
b) \(4x^8+1=4x^8+4x^4+1-4x^4=\left(2x^4+1\right)^2-4x^4=\left(2x^4-2x^2+1\right)\left(2x^4+2x^2+1\right)\)
d) \(x^2+14x+48=\left(x+7\right)^2-1=\left(x+7+1\right)\left(x+7-1\right)=\left(x+8\right)\left(x+6\right)\)
NV
0
U
1
11 tháng 12 2015
\(=\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16\)
\(=\left(x+6\right)\left(x+4\right)\left(x+2\right)\left(x+8\right)+16\)
\(=\left(x^2+10x+24\right)\left(x^2+10x+16\right)+16\)
\(=\left(t+8\right)t+16=\left(t+4\right)^2=\left(x^2+10x+20\right)^2\)
26 tháng 9 2018
\(x^3-x^2-14x+24\)
\(=x^3-2x^2+x^2-2x-12x+24\)
\(=x^2\left(x-2\right)+x\left(x-2\right)-12\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+x-12\right)\)
\(=\left(x-2\right).\left[x^2+4x-3x-12\right]\)
\(=\left(x-2\right).\left[x\left(x+4\right)-3\left(x+4\right)\right]\)
\(=\left(x-2\right)\left(x+4\right)\left(x-3\right)\)
\(x^4+x^3+2x-4\)
\(=x^4-x^3+2x^3-2x^2+2x^2-2x+4x-4\)
\(=x^3\left(x-1\right)+2x^2\left(x-1\right)+2x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3+2x^2+2x+4\right)\)
\(=\left(x-1\right).\left[x^2\left(x+2\right)+2\left(x+2\right)\right]\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+2\right)\)
\(8x^4-2x^3-3x^2-2x-1\)
\(=8x^4-8x^3+6x^3-6x^2+3x^2-3x+x-1\)
\(=8x^3\left(x-1\right)+6x^2\left(x-1\right)+3x\left(x-1\right)+x-1\)
\(=\left(x-1\right)\left(8x^3+6x^2+3x+1\right)\)
\(=\left(x-1\right)\left[\left(8x^3+1\right)+\left(6x^2+3x\right)\right]\)
\(=\left(x-1\right)\left[\left(2x+1\right)\left(4x^2-2x+1\right)+3x\left(2x+1\right)\right]\)
\(=\left(x-1\right)\left(2x+1\right)\left(4x^2+x+1\right)\)
\(3x^2-7x+2\)
\(=3x^2-6x-x+2\)
\(=3x\left(x-2\right)-\left(x-2\right)\)
\(=\left(x-2\right)\left(3x-1\right)\)
Chúc bạn học tốt.
NP
3
3 tháng 2 2019
\(x^3-x^2-14x+24\)
\(=x^3-2x^2+x^2-2x-12x+24\)
\(=x^2\left(x-2\right)+x\left(x-2\right)-12\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+x-12\right)\)
\(=\left(x-2\right)\left(x^2+4x-3x-12\right)\)
\(=\left(x-2\right)\left[x\left(x+4\right)-3\left(x+4\right)\right]\)
\(=\left(x-2\right)\left(x+4\right)\left(x-3\right)\)
3 tháng 2 2019
Ta có:\(x^3-x^2-14x+24=\left(x^3-2x^2\right)+\left(x^2-2x\right)-\left(12x-24\right)\)
\(=x^2\left(x-2\right)+x\left(x-2\right)-12\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+x-12\right)\)
\(=\left(x-2\right)\left(x^2-3x+4x-12\right)\)
\(=\left(x-2\right)\left[x\left(x-3\right)+4\left(x-3\right)\right]\)
\(=\left(x-2\right)\left(x+4\right)\left(x-3\right)\)
5 tháng 7 2016
a) \(x^2+4x+3=\left(x^2+4x+4\right)-1=\left(x+2\right)^2-1^2=\left(x+1\right)\left(x+3\right)\) (mình sửa lại)
b) \(x^2+8x-9=\left(x^2+8x+16\right)-25=\left(x+4\right)^2-5^2=\left(x-1\right)\left(x+9\right)\)
c) \(3x^2+6x-9=3\left[\left(x^2+2x+1\right)-4\right]=3\left[\left(x+1\right)^2-2^2\right]=3\left(x-1\right)\left(x+3\right)\)
d) \(2x^2+x-3=2x^2-4x+2+5x-5=2\left(x^2-2x+1\right)+5\left(x-1\right)=2\left(x-1\right)^2+5\left(x-1\right)=\left(x-1\right)\left(2x+3\right)\)
KL
5
KL
19 tháng 9 2018
Mình nhầm 1 chút nhé mọi người \(x^2-8x-9\) nhé!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
c) x2 - 8x - 9
= x2 + x - 9x - 9
= x.(x+1) - 9.(x+1)
= (x+1).(x-9)
d) x2 + 14x + 48
= x2 + 8x + 6x + 48
= x.(x+8) + 6.(x+8)
= (x+8).(x+6)
c/ \(x^2-8x-9=\left(x^2+x\right)-\left(9x+9\right)=x\left(x+1\right)-9\left(x+1\right)=\left(x+1\right)\left(x-9\right)\)
d/ \(x^2+14x+48=x^2+6x+8x+48=x\left(x+6\right)+8\left(x+6\right)=\left(x+6\right)\left(x+8\right)\)