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29 tháng 9 2018
a, \(x^3+4x^2-29x+24\)
\(=x^3-x^2+5x^2-5x-24x+24\)
\(=x^2\left(x-1\right)+5x\left(x-1\right)-24\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+5x-24\right)\)
\(=\left(x-1\right)\left[x\left(x-3\right)+8\left(x-3\right)\right]\)
\(=\left(x-1\right)\left(x-3\right)\left(x+8\right)\)
\(x^3+6x^2+11x+6\)
\(=x^3+x^2+5x^2+5x+6x+6\)
\(=x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+5x+6\right)\)
\(=\left(x+1\right)\left[x\left(x+2\right)+3\left(x+2\right)\right]\)
\(=\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
Chúc bạn học tốt.
LN
3
5 tháng 7 2018
\(x^3+6x^2+11x+6=x^3+x^2+5x^2+5x+6x+6\)
\(=x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)=\left(x+1\right)\left(x^2+5x+6\right)\)
\(=\left(x+1\right)\left(x^2+2x+3x+6\right)=\left(x+1\right)\left[x\left(x+2\right)+3\left(x+2\right)\right]\)
\(=\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
VT
1
ZR
12 tháng 10 2015
x^3 + 6x^2 + 11x + 6
= x^3 + x^2 + 5x^2 + 5x + 6x + 6
= x^2(x + 1) + 5x(x + 1) + 6(x + 1)
= (x + 1)(x^2 + 5x + 6)
= (x + 1)(x^2 + 2x + 3x + 6)
= (x + 1)[x(x + 2) + 3(x + 2)
= (x + 1)(x + 2)(x + 3)
VT
0
NM
1
3 tháng 9 2015
ta co: \(F\left(x\right)=x^3-6x^2+11x-6\)
\(=x^3-x^2-5x^2+5x+6x-6\)
\(=x^2\left(x-1\right)-5x\left(x-1\right)+6x\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-5x+6\right)\)
\(=\left(x-1\right)\left(x^2-2x-3x+6\right)\)
\(=\left(x-1\right)\left(x-2\right)\left(x-3\right)\)
S
23 tháng 12 2016
a, \(x^4+6x^3+7x^2-6x+1\)
\(=x^4-2x^2+1+6x^3+9x^2+6x\)
\(=\left(x^2-1\right)^2+6x\left(x^2-1\right)+9x^2\)
\(=\left(x^2-1+3x\right)^2\)
b, \(x^4-7x^3+14x^2-7x+1\)
\(=x^4+2x^2+1+7x^3+12x^2-7x\)
\(=\left(x^2+1\right)^2-7x\left(x^2+1\right)+12^2\)
\(=\left(x^2-1+3x\right)^2\)
c, \(12x^2-11x-36\)
\(=12x^2-27x+16x-36\)
\(=3x\left(4x-9\right)+4\left(4x-9\right)\)
\(=\left(4x-9\right)\left(3x+4\right)\)
16 tháng 2 2019
1) \(x^3+6x^2+11x+6\)
\(=x^3+x^2+5x^2+5x+6x+6\)
\(=x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+5x+6\right)\)
\(=\left(x+1\right)\left(x^2+2x+3x+6\right)\)
\(=\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
17 tháng 2 2019
2) \(A=n^3\left(n^2-7\right)^2-36n\)
\(A=n\left[n^2\left(n^2-7\right)^2-36\right]\)
\(A=n\left\{\left[n\left(n^2-7\right)\right]^2-6^2\right\}\)
\(A=n\left(n^3-7n-6\right)\left(n^3-7n+6\right)\)
\(A=n\left(n^3-7n-6\right)\left(n^3-n-6n+6\right)\)
\(A=n\left(n^3-7n-6\right)\left[n\left(n-1\right)\left(n+1\right)-6\left(n-1\right)\right]\)
\(A=n\left(n^3-7n-6\right)\left(n-1\right)\left(n^2+n-6\right)\)
\(A=n\left(n-1\right)\left(n^3-7n-6\right)\left(n^2+3n-2n-6\right)\)
\(A=n\left(n-1\right)\left(n^3-7n-6\right)\left[n\left(n+3\right)-2\left(n+3\right)\right]\)
\(A=n\left(n-1\right)\left(n-2\right)\left(n+3\right)\left(n^3-7n-6\right)\)
\(A=n\left(n-1\right)\left(n-2\right)\left(n+3\right)\left(n^3-n-6n-6\right)\)
\(A=n\left(n-1\right)\left(n-2\right)\left(n+3\right)\left[n\left(n-1\right)\left(n+1\right)-6\left(n+1\right)\right]\)
\(A=n\left(n-1\right)\left(n-2\right)\left(n+3\right)\left(n+1\right)\left(n^2+n-6\right)\)
\(A=n\left(n-1\right)\left(n-2\right)\left(n+3\right)\left(n+1\right)\left(n^2+3n-2n-6\right)\)
\(A=n\left(n-1\right)\left(n-2\right)\left(n+3\right)\left(n+1\right)\left[n\left(n+3\right)-2\left(n+3\right)\right]\)
\(A=n\left(n-1\right)\left(n-2\right)\left(n+3\right)\left(n+1\right)\left(n+3\right)\left(n-2\right)\)
\(A=\left(n-1\right)n\left(n+1\right)\left(n-2\right)^2\left(n+3\right)^2\)
Rồi sao nữa còn nghĩ :))
LG
1
19 tháng 7 2016
6x3-11x2+x+4
=6x2-12x2+6x+x2-5x+4
=6x.(x2-2x+1)+x2-4x-x+4
=6x.(x-1)2+x.(x-4)-(x-4)
=6x.(x-1)2+(x-4)(x-1)
=(x-1)[6x.(x-1)+x-4]
=(x-1)(6x2-6x+x-4)
=(x-1)(6x2+3x-8x-4)
=(x-1)[3x.(2x+1)-4.(2x+1)]
=(x-1)(2x+1)(3x-4)
19 tháng 8 2017
a, \(6x^2-xy-y^2\)
\(=6x^2-3xy+2xy-y^2\)
\(=3x\left(2x-y\right)+2y\left(x-y\right)\)
\(=\left(3x+2y\right)\left(x-y\right)\)
b, \(8x^2-23x-3\)
\(=8x^2-24x+x-3\)
\(=8x\left(x-3\right)+\left(x-3\right)=\left(8x+1\right)\left(x-3\right)\)
c, \(10x^2-11x-6\)
\(=10x^2-15x+4x-6\)
\(=5x\left(2x-3\right)+2\left(2x-3\right)\)
\(=\left(5x+2\right)\left(2x-3\right)\)
d, \(x^3-6x^2+11x-6\)
\(=x^3-3x^2-3x^2+9x+2x-6\)
\(=x^2\left(x-3\right)-3x\left(x-3\right)+2\left(x-3\right)\)
\(=\left(x^2-3x+2\right)\left(x-3\right)\)
\(=\left(x^2-2x-x+2\right)\left(x-3\right)\)
\(=\left(x-1\right)\left(x-2\right)\left(x-3\right)\)
\(x^3+3.x^2.2+3.x.2^2+2^2-x+2=\left(x+2\right)^3-\left(x+2\right)=\left(x+2\right)\left(\left(x-2\right)^2-1\right)\)
x3+6x2+11x+6
= x3+3x2+3x2+9x+2x+6
=x2(x+3)+ 3x(x+3)+2(x+3)
=(x+3)(x2+3x+2)