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PV
3
KN
20 tháng 6 2019
\(x^3-2x^2-5x+6\)
\(=\left(x^3-4x^2+3x\right)+\left(2x^2-8x+6\right)\)
\(=x\left(x^2-4x+3\right)+2\left(x^2-4x+3\right)\)
\(=\left(x+2\right)\left(x^2-4x+3\right)\)
55
20 tháng 6 2019
1. \(x^3-2x-5x+6\)
\(\Leftrightarrow x^2\left(x-3\right)+x\left(x-3\right)-2\left(x-3\right)\)
\(\Leftrightarrow\left(x-3\right)\left(x^2+x-2\right)\)
\(\Leftrightarrow\left(x-3\right)\left(x+2\right)\left(x-1\right)\)
2. \(x^3-7x^2+15x-9\)
\(\Leftrightarrow\left(x^3-x^2\right)-\left(6x^2-6x\right)+\left(9x-9\right)\)
\(\Leftrightarrow x^2\left(x-1\right)-6x\left(x-1\right)+9\left(x-1\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-6x+9\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x\left(x-3\right)-3\left(x-3\right)\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)^2\)
HN
3
11 tháng 9 2018
1, <=> \(\left(4x\right)^2-\left(9y\right)^2\)=\(\left(4x-9y\right)\left(4x+9y\right)\)
T
11 tháng 9 2018
1) \(16x^2-81.y^2=\left(4x\right)^2-\left(9.y\right)^2=\left(4x-9y\right)\left(4x+9y\right)\)
2) \(\left(5x-3y\right)^2-\left(3x-5y\right)^2=\left(5x-3y-3x+5y\right)\left(5x-3y+3x-5y\right)=\left(2x+2y\right).\left(8x-8y\right)\)
\(=16.\left(x+y\right)\left(x-y\right)\)
3)\(4x^2-y^2+4y-4=4x^2-\left(y^2-4y+4\right)=\left(2x\right)^2-\left(y-2\right)^2=\left(2x-y+2\right).\left(2x+y-2\right)\)
4)\(9.\left(x-y\right)^2-16.\left(2x+y\right)^2=3^2.\left(x-y\right)^2-4^2.\left(2x+y\right)^2=\left(3x-3y\right)^2-\left(8x+4y\right)^2\)
\(=\left(3x-3y-8x-4y\right)\left(3x-3y+8x+4y\right)=\left(-5x-7y\right).\left(11x+y\right)\)
VT
1
14 tháng 8 2019
\(2x^2\left(x-1\right)+3x^2-3x-2x+2.\)
\(2x^2\left(x-1\right)+3x\left(x-1\right)-2\left(x-1\right)\)
\(\left(x-1\right)\left(2x^2+3x-2\right)\)
\(2\left(x-1\right)\left(x^2+\frac{3}{2}x-2\right)=2\left(x-1\right)\left\{\left(x^2+\frac{2x.3}{4}+\frac{9}{16}\right)-\left(2+\frac{9}{16}\right)\right\}\)
\(2\left(x-1\right)\left\{\left(x+\frac{3}{4}\right)^2-\left(2+\frac{9}{16}\right)\right\}=2\left(x-1\right)\left\{\left(x+\frac{3}{4}-2-\frac{9}{16}\right)\left(x+\frac{3}{4}+2+\frac{9}{16}\right)\right\}\)
14 tháng 8 2019
\(=2x^3+4x^2-3x^2-6x+x+2\)
= \(2x^2\left(x+2\right)-3x\left(x+2\right)+\left(x+2\right)\)
= \(\left(x+2\right)\left(2x^2-3x+1\right)\)
= \(\left(x+2\right)\left(2x^2-x-2x+1\right)\)
= \(\left(x+2\right)\left(2x\left(x-1\right)-\left(x-1\right)\right)\)
= \(\left(x+2\right)\left(x-1\right)\left(2x-1\right)\)
27 tháng 12 2014
Ta có:\(2x^3-x^2+5x+3=2x^3+x^2-2x^2-x+6x+3=2x^2\left(x+0,5\right)-2x\left(x+0,5\right)+6\left(x+0,5\right)=\left(2x^2-2x+6\right)\left(x+0,5\right)\)
TT
0
NP
2
LH
19 tháng 11 2015
4x4 + 4x3 + 5x2 + 2x +1
= (4x4 + 4x3 + x2 ) + ( 2x2 + 1 ) + 1
= x2(2x + 1 )2 + 2x(2x + 1) +1
= (x(2x + 1 ) + 1)2
= (2x + x + 1)2
NC
6
27 tháng 2 2015
4x4+4x3+5x2+2x+1
=(4x4+4x3+x2) + (2x2+1) +1
= x2(2x+1)2 + 2x(2x+1) +1
= (x(2x+1)+1)2
=(2x2+x+1)2
TN
19 tháng 7 2017
\(2x^3-x^2+5x+3\)
\(=2x^3-2x^2+6x+x^2-x+3\)
\(=2x\left(x^2-x+3\right)+\left(x^2-x+3\right)\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
\(16\left(2x+3\right)^2-9\left(5x-2\right)^2\)
\(=\left[4\left(2x+3\right)\right]^2-\left[3\left(5x-2\right)\right]^2\)
\(=\left[4\left(2x+3\right)-3\left(5x-2\right)\right]\left[4\left(2x+3\right)+3\left(5x-2\right)\right]\)
\(=\left(-7x+18\right)\left(23x+6\right)\)