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NT
0
KT
16 tháng 7 2018
1) \(x^6-x^4-9x^3+9x^2\)
\(=x^2\left(x^4-x^2-9x+9\right)\)
\(=x^2\left[x^2\left(x^2-1\right)-9\left(x-1\right)\right]\)
\(=x^2\left(x-1\right)\left[x^2\left(x+1\right)-9\right]\)
\(=x^2\left(x-1\right)\left(x^3+x^2-9\right)\)
2) \(x^4-4x^3+8x^2-16x+16\)
\(=x^2\left(x^2+4\right)-4x\left(x^2+4\right)+4\left(x^2+4\right)\)
\(=\left(x^2+4\right)\left(x-2\right)^2\)
18 tháng 7 2018
3) \(x^4-25x^2+20x-4=x^4+5x^3-2x^2-5x^3-25x^2+10x+2x^2+10x-4\)
\(=x^2\left(x^2+5x-2\right)-5x\left(x^2+5x-2\right)+2\left(x^2+5x-2\right)\)
\(=\left(x^2+5x-2\right)\left(x^2-5x+2\right)\)
4) \(5x\left(x-2y\right)+2\left(2y-x\right)^2\)\(=5x\left(x-2y\right)+2\left(x-2y\right)^2=\left(x-2y\right)\left(5x+2x-4y\right)=\left(x-2y\right)\left(7x-4y\right)\)
5) \(x^2\left(x^2-6\right)-x^2+9=x^4-7x^2+9\)
\(=x^4+x^3-3x^2-x^3-x^2+3x-3x^2-3x+9\)
\(=x^2\left(x^2+x-3\right)-x\left(x^2+x-3\right)-3\left(x^2+x-3\right)\)
\(=\left(x^2+x-3\right)\left(x^2-x-3\right)\)
6) \(7x\left(y-4\right)^2-\left(4-y\right)^3=7x\left(y-4\right)^2+\left(y-4\right)^3=\left(y-4\right)^2\left(7x+y-4\right)\)
7) \(x^3+2x^2-6x-27=x^3-3x^2+5x^2-15x+9x-27\)
\(=x^2\left(x-3\right)+5x\left(x-3\right)+9\left(x-3\right)=\left(x-3\right)\left(x^2+5x+9\right)\)
PA
16 tháng 10 2016
\(2x^2+3x-27=2x^2-6x+9x-27=2x\left(x-3\right)+9\left(x-3\right)=\left(2x+9\right)\left(x-3\right)\)
\(x^3-7x+6=x^3-x-6x+6=x\left(x^2-1\right)-6\left(x-1\right)=x\left(x-1\right)\left(x+1\right)-6\left(x-1\right)=\left(x-1\right)\left(x^2+x-6\right)\)
\(x^3+5x^2+8x+4=x^3+x^2+4x^2+8x+4=x^2\left(x+1\right)+4\left(x^2+2x+1\right)=x^2\left(x+1\right)+4\left(x+1\right)^2\)
\(=\left(x+1\right)\left(x^2+4x+4\right)=\left(x+1\right)\left(x+2\right)^2\)
\(27x^3-27x^2+18x-4=27x^3-9x^2-18x^2+6x+12x-4\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)=\left(3x-1\right)\left(9x^2-6x+4\right)\)
9 tháng 10 2018
a, 4x2 - 12x + 9
= (2x + 3)2
b, 9x4y3 + 3x2y4
= 3x2y3(3x2 + y)
c, ( x - 3 )2 - 2x ( x - 3 )
= (x - 3)(x - 3 - 2x)
= (x - 3)(-x - 3)
d, 3x ( x - 1 ) + 6 ( x - 1 )
= 3(x - 1)(x + 2)
e, 2x ( x + 1 ) - 4x - 4
= 2x(x + 1) - 4(x + 1)
= (x + 1)(2x - 4)
= 2(x + 1)(x - 2)
f, ( 2x - 3 )2 - 4x + 6
= (2x - 3)2 - 2(2x - 3)
= (2x - 3)(2x - 3 - 2)
= (2x - 3)(2x - 5)
AV
6
9 tháng 10 2016
d) \(x^4+4=x^4+4x^2+4-4x^2=\left(x^2+2\right)-\left(2x\right)^2=\left(x^2+2x+2\right)\left(x^2-2x+2\right)\)
CN
1
20 tháng 10 2019
a) 4x2 - 20x + 25 - 36y2
= (2x - 5)2 - 36y2
= (2x - 5 - 6y)(2x - 5 + 6y)
b) x3 + x2 - 2x - 8
= (x3 - 8) + (x2 - 2x)
= (x - 2)(x2 + 2x + 4) + x(x - 2)
= (x - 2)(x2 + 2x + 4 + x)
= (x - 2)(x2 + 3x + 4)
d) x4 + 6x3 + 9x2 - 16
= x2(x2 + 6x + 9) - 16
= x2(x + 3)2 - 16
= (x2 + 3x)2 - 16
= (x2 + 3x - 4)(x2 + 3x + 4)
= (x2 + 4x - x - 4)(x2 + 3x + 4)
= [x(x + 4) - (x + 4)](x2 + 3x + 4)
= (x - 1)(x + 4)(x2 + 3x + 4)
PA
30 tháng 10 2016
\(x^3-x^2-5x+125\)
\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2-5x+25-x\right)\)
\(=\left(x+5\right)\left(x^2-6x+25\right)\)
\(x^6-x^4-9x^3+9x^2\)
\(=x^4\left(x^2-1\right)-9x^2\left(x-1\right)\)
\(=x^4\left(x-1\right)\left(x+1\right)-9x^2\left(x-1\right)\)
\(=x^2\left(x-1\right)\left[x^2\left(x+1\right)-9\right]\)
\(=x^2\left(x-1\right)\left(x^3+x^2-9\right)\)
\(x^4-4x^3+8x^2-16x+16\)
\(=\left(x^2+4\right)^2-4x\left(x^2+4\right)\)
\(=\left(x^2+4\right)\left(x^2+4-4x\right)\)
\(=\left(x^2+4\right)\left(x-2\right)^2\)
\(3a^2-6ab+3b^2-12c^2\)
\(=3\left(a^2-2ab+b^2-4c^2\right)\)
\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]\)
\(=3\left(a-b+2c\right)\left(a-b-2c\right)\)
a) \(x^2\left(x-3\right)+27-9x=0\)
\(x^2\left(x-3\right)+9\left(3-x\right)=0\)
\(x^2\left(x-3\right)-9\left(x-3\right)=0\)
\(\left(x^2-9\right)\left(x-3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x^2-9=0\\x-3=0\end{cases}}\Rightarrow\orbr{\begin{cases}x^2=9\\x=3\end{cases}}\Rightarrow\orbr{\begin{cases}x=3\\x=3\end{cases}}\Rightarrow x=3\)
vay \(x=3\)
a) \(x^2-4x+3\)
= \(x^2-3x-x+3\)
\(=\left(x^2-3x\right)-\left(x-3\right)\)
\(=x\left(x-3\right)-\left(x-3\right)\)
\(=\left(x-1\right)\left(x-3\right)\)
a)\(x^2-4x+3=x^2-3x-x+3=x\left(x-3\right)-\left(x-3\right)=\left(x-3\right)\left(x-1\right)\)
b)\(x^2+x-6=x^2+3x-2x-6=x\left(x+3\right)-2\left(x+3\right)=\left(x-2\right)\left(x+3\right)\)
c)\(x^2-5x+6=x^2-2x-3x+6=x\left(x-2\right)-3\left(x-2\right)=\left(x-3\right)\left(x-2\right)\)
d)\(x^4+4=x^4+4x^2+4-4x^2=\left(x^2+2\right)^2-\left(2x\right)^2=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)