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KT
2 tháng 11 2018
\(x^8+x+1\)
\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)
\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)
TA
4
KT
29 tháng 10 2018
\(x^8+x^7+1\)
\(=\left(x^8-x^6+x^5-x^3+x^2\right)+\left(x^7-x^5+x^4-x^2+x\right)+\left(x^6-x^4+x^3-x+1\right)\)
\(=x^2\left(x^6-x^4+x^3-x+1\right)+x\left(x^6-x^4+x^3-x+1\right)+\left(x^6-x^4+x^3-x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)
DT
1
19 tháng 11 2016
a, x8 + x7 + 1
=x2 (x6 - 1) + x (x6 - 1) +(x2 + x + 1)
= (x6 _ 1)(x2 + x) + (x2 + x +1)
= (x3 - 1)(x3 + 1)( x2 + x) + (x2 + x +1)
=(x - 1)(x2 + x +1)( x2 + x) + (x2 + x +1)
=(x2 + x +1)((x - 1)( x2 + x) +1)
=(x2 + x +1)(x3 + 1)
b, x5 - x4-1
c, x7+x5 + 1
d,x8 + x4 +1
Chú ý: Các đa thức có dạng: x3m+1+x3n+2+1 như x7+x2+1; x7+x5+1; x8 + x4 +1;
x5+x+1; x8+x+1 đều có nhân tử chung là x2 + x +1
Các phần còn lại tương tự nhé!!!
MT
3
25 tháng 5 2015
a) x8 + x + 1 = (x^2+x+1)*(x^6-x^5+x^3-x^2+1)
b) x^8 + 3x^4 + 4 = (x^4-x^2+2)*(x^4+x^2+2)
NT
3
MT
22 tháng 8 2015
a) x7+ x2 + 1
=x7-x+x2+x+1
=x.(x6-1)+(x2+x+1)
=x.(x3-1)(x3+1)+(x2+x+1)
=x.(x-1)(x2+x+1)(x3+1)+(x2+x+1)
=(x2+x+1)[x.(x-1)(x3+1)+1]
=(x2+x+1)(x5+x2-x4-x+1)
b) x5 + x4 + 1
=x5+x4+x3+x2+x+1-x3-x2-x
=x3.(x2+x+1)+(x2+x+1)-x.(x2+x+1)
=(x2+x+1)(x3+1-x)
12 tháng 8 2019
\(a,x^4+4=x^4+4x^2+4-2x^4=\left(x^2+2\right)^2-4x^2\)
\(=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)
\(b,4x^8+1=4x^8+4x^4+1-4x^4\)
\(=\left(2x^4+1\right)^2-4x^4=\left(2x^4-2x^2+1\right)\left(2x^4+2x^2+1\right)\)
\(c,4x^4+y^4=4x^4+4x^2y^2+y^4-4x^2y^2\)
\(=\left(2x^2+y^2\right)^2-4x^2y^2\)
\(=\left(2x^2+y^2-2xy\right)\left(2x^2+y^2+2xy\right)\)
KT
18 tháng 7 2018
a) \(x^4+324=\left(x^2-6x+18\right)\left(x^2+6x+18\right)\)
c) \(x^{13}+x^5+1=\left(x^2+x+1\right)\left(x^{11}-x^{10}+x^8-x^7+x^5-x^4+x^3-x+1\right)\)
d) \(x^{11}+x+1=\left(x^2+x+1\right)\left(x^9-x^8+x^6-x^5+x^3-x^2+1\right)\)
e) \(x^8+3x^4+4=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)
AT
2
MT
9 tháng 7 2015
a) 4x2 - 17xy + 13y2
=4x2-4xy-13xy+13y2
=4x(x-y)-13y(x-y)
=(x-y)(4x-13y)
b) x8 + x4 +1
=x8+2x4+1-x4
=(x4+1)2-x4
=(x4+1-x2)(x4+1+x2)
S
27 tháng 7 2018
a, \(x^8+x^7+1=x^8-x^2+x^7-x+x^2+x+1=x^2\left(x^6-1\right)+x\left(x^6-1\right)+\left(x^2+x+1\right)\)
\(=x^2\left(x^3-1\right)\left(x^3+1\right)+x\left(x^3-1\right)\left(x^3+1\right)+\left(x^2+x+1\right)\)
\(=x^2\left(x-1\right)\left(x^2+x+1\right)\left(x^3+1\right)+x\left(x-1\right)\left(x^2+x+1\right)\left(x^3+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left[x^2\left(x-1\right)\left(x^3+1\right)+x\left(x-1\right)\left(x^3+1\right)+1\right]\)
\(=\left(x^2+x+1\right)\left[\left(x^3-x^2\right)\left(x^3+1\right)+\left(x^2-x\right)\left(x^3+1\right)+1\right]\)
\(=\left(x^2+x+1\right)\left(x^6+x^3-x^5-x^2+x^5+x^2-x^4-x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)
b, \(x^8+x^4+1=x^8+2x^4+1-x^4=\left(x^4+1\right)^2-x^4=\left(x^4-x^2+1\right)\left(x^4+x^2+1\right)\)
\(=\left(x^4-x^2+1\right)\left(x^4+2x^2+1-x^2\right)=\left(x^4-x^2+1\right)\left[\left(x^2+1\right)-x^2\right]=\left(x^4-x^2+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)\)
c, \(x^5+x+1=x^5-x^2+x^2+x+1=x^2\left(x^3-1\right)+\left(x^2+x+1\right)=x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)
\(x^8+x^4+1\)
\(=x^8+2x^4+1-x^4\)
\(=\left(x^4+1\right)^2-x^4\)
\(=\left(x^4+x^2+1\right)\left(x^4-x^2+1\right)\)
\(=\left(x^2-x+1\right)\left(x^2+x+1\right)\left(x^4-x^2+1\right)\)
\(=\left(x^2-x+1\right)\left(x^2+x+1\right)\left(x^4-x^2+1\right)\)
\(x^5+x+1\)
\(=x^5-x^4+x^2+x^4-x^3+x+x^3-x^2+1\)
\(=x^2\left(x^3-x^2+1\right)+x\left(x^3-x^2+1\right)+\left(x^3-x^2+1\right)\)
\(=\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)