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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
TN
19 tháng 7 2017
\(2x^3-x^2+5x+3\)
\(=2x^3-2x^2+6x+x^2-x+3\)
\(=2x\left(x^2-x+3\right)+\left(x^2-x+3\right)\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
BN
0
LC
0
ND
2
30 tháng 4 2017
a) \(45+x^3-5x^2-9x\)
\(\Leftrightarrow\left(45-9x\right)+\left(x^3-5x^2\right)\)
\(\Leftrightarrow-9\left(x-5\right)+x^2\left(x-5\right)\)
\(\Leftrightarrow\left(x-5\right)\left(x-3\right)\left(x+3\right)\)
TK NKA !!!
TM
2
23 tháng 6 2016
\(^{x^3-6x^2-x+30=x^3-5x^2-3x^2+15x-2x^2-10x-6x+30}\)
=x^2(x-5)-3x(x-5)-2x(x-5)-6(x-5)
=(x-5)(x^2-3x-2x-6)
=(x-5)[x(x-3)-2(x-3)]
=(x-5)(x-3)(x-2)
27 tháng 10 2019
\(x^3-6x^2-x+30\)
= \(x^3-5x^2-3x^2+15x+2x^2-10x-6x+30\)
= \(x^2\left(x-5\right)-3x\left(x-5\right)+2x\left(x-5\right)-6\left(x-5\right)\)
= \(\left(x-5\right)\left(x^2-3x+2x-6\right)\)
= \(\left(x-5\right)\left(x\left(x-3\right)+2\left(x-3\right)\right)\)
= \(\left(x-5\right)\left(x+2\right)\left(x-3\right)\)
TM
1
1 tháng 7 2016
a)\(=x^3+2x^2-8x^2-16x+15x+30\)
\(=x^2\left(x+2\right)-8x\left(x+2\right)+15\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-8x+15\right)\)
\(=\left(x+2\right)\left(x^2-5x-3x+15\right)\)
\(=\left(x+2\right)\left[x\left(x-5\right)-3\left(x-5\right)\right]\)
\(=\left(x+2\right)\left(x-5\right)\left(x-3\right)\)
nha
KN
3 tháng 7 2019
\(x^8+3x^4+4\)
\(=\left(x^8-x^6+2x^4\right)+\left(x^6-x^4+2x^2\right)+\left(2x^4-2x^2+4\right)\)
\(=x^4\left(x^4-x^2+2\right)+x^2\left(x^4-x^2+2\right)+2\left(x^4-x^2+2\right)\)
\(=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)
KN
3 tháng 7 2019
\(4x^4+4x^3+5x^2+2x+1\)
\(=\left(4x^4+2x^3+2x^2\right)+\left(2x^3+x^2+x\right)+\left(2x^2+x+1\right)\)
\(=2x^2\left(2x^2+x+1\right)+x\left(2x^2+x+1\right)+\left(2x^2+x+1\right)\)
\(=\left(2x^2+x+1\right)^2\)
\(2x^2\left(x-1\right)+3x^2-3x-2x+2.\)
\(2x^2\left(x-1\right)+3x\left(x-1\right)-2\left(x-1\right)\)
\(\left(x-1\right)\left(2x^2+3x-2\right)\)
\(2\left(x-1\right)\left(x^2+\frac{3}{2}x-2\right)=2\left(x-1\right)\left\{\left(x^2+\frac{2x.3}{4}+\frac{9}{16}\right)-\left(2+\frac{9}{16}\right)\right\}\)
\(2\left(x-1\right)\left\{\left(x+\frac{3}{4}\right)^2-\left(2+\frac{9}{16}\right)\right\}=2\left(x-1\right)\left\{\left(x+\frac{3}{4}-2-\frac{9}{16}\right)\left(x+\frac{3}{4}+2+\frac{9}{16}\right)\right\}\)
\(=2x^3+4x^2-3x^2-6x+x+2\)
= \(2x^2\left(x+2\right)-3x\left(x+2\right)+\left(x+2\right)\)
= \(\left(x+2\right)\left(2x^2-3x+1\right)\)
= \(\left(x+2\right)\left(2x^2-x-2x+1\right)\)
= \(\left(x+2\right)\left(2x\left(x-1\right)-\left(x-1\right)\right)\)
= \(\left(x+2\right)\left(x-1\right)\left(2x-1\right)\)