PTBĐTTNT bằng p2 thêm bớt hạng dư
1/ 4x4+81
2/ 4a4+b4
3/ x7+x5+1
4/ x5 +x4+1
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AH
Akai Haruma
Giáo viên
7 tháng 7 2021
a. $6x^2-11x=x(6x-11)$
b. $x^7+x^5+1=(x^7-x)+(x^5-x^2)+x+x^2+1$
$=x(x^6-1)+x^2(x^3-1)+(x^2+x+1)$
$=x(x^3-1)(x^3+1)+x^2(x^3-1)+(x^2+x+1)$
$=(x^3-1)(x^4+x+x^2)+(x^2+x+1)$
$=(x-1)(x^2+x+1)(x^4+x^2+x)+(x^2+x+1)$
$=(x^2+x+1)[(x-1)(x^4+x^2+x)+1]$
$=(x^2+x+1)(x^5-x^4+x^3-x+1)$
AH
Akai Haruma
Giáo viên
7 tháng 7 2021
c.
$x^8+x^4+1=(x^4)^2+2.x^4+1-x^4$
$=(x^4+1)^2-(x^2)^2$
$=(x^4+1-x^2)(x^4+1+x^2)$
$=(x^4+1-x^2)(x^4+2x^2+1-x^2)$
$=(x^4-x^2+1)[(x^2+1)^2-x^2]$
$=(x^4-x^2+1)(x^2+1-x)(x^2+1+x)$
d.
$x^3-5x+8-4=x^3-5x+4$
$=x^3-x^2+x^2-x-(4x-4)$
$=x^2(x-1)+x(x-1)-4(x-1)=(x-1)(x^2+x-4)$
e.
$x^5+x^4+1=(x^5-x^2)+(x^4-x)+x^2+x+1$
$=x^2(x^3-1)+x(x^3-1)+x^2+x+1$
$=(x^3-1)(x^2+x)+(x^2+x+1)$
$=(x-1)(x^2+x+1)(x^2+x)+(x^2+x+1)$
$=(x^2+x+1)[(x-1)(x^2+x)+1]$
$=(x^2+x+1)(x^3-x+1)$
12 tháng 7 2023
\(a,=\left(5x^3+10x\right)+\left(x^4-4\right)\\ =5x\left(x^2+2\right)+\left(x^2+2\right)\left(x^2-2\right)\\ =\left(x^2+2\right)\left(x^2+5x-2\right)\\ b,=\left(x+y\right)^3-3xy\left(x+y\right)+z^3-3xyz\\ =\left[\left(x+y\right)^3+z^3\right]-3xy\left(x+y+z\right)\\ =\left(x+y+z\right)\left[\left(x+y\right)^2-z\left(x+y\right)+z^2\right]-3xy\left(x+y+z\right)\\ =\left(x+y+z\right)\left(x^2+2xy+y-xz-yz+z^2-3xy\right)\\ =\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)
\(c,=\left(x^8+x^7+x^6\right)-\left(x^7+x^6+x^5\right)+\left(x^5+x^4+x^3\right)-\left(x^4+x^3+x^2\right)+\left(x^2+x+1\right)\\ =\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\\ d,=\left(x^7+x^6+x^5\right)-\left(x^6+x^5+x^4\right)+\left(x^4+x^3+x^2\right)-\left(x^3+x^2+x\right)+\left(x^2+x+1\right)\\ =\left(x^2+x+1\right)\left(x^5-x^4+x^2-x+1\right)\\ e,=\left(x^{10}+x^9+x^8\right)-\left(x^9+x^8+x^7\right)+\left(x^7+x^6+x^5\right)-\left(x^6+x^5+x^4\right)+\left(x^5+x^4+x^3\right)-\left(x^3+x^2+x\right)+\left(x^2+x+1\right)\\ =\left(x^2+x+1\right)\left(x^{10}-x^7+x^5-x^4+x^3-x+1\right)\)
12 tháng 7 2023
a: =x^4+2x^2+5x^3+10x-2x^2-4
=(x^2+2)(x^2+5x-2)
b; =(x+y)^3+z^3-3xy(x+y)-3xyz
=(x+y+z)*(x^2+2xy+y^2-xz-yz+z^2)-3xy(x+y+z)
=(x+y+z)(x^2+y^2+z^2-xy-yz-xz)
c: =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^2+x+1)(x^6-x^5+x^3-x^2+1)
PT
1
CM
4 tháng 7 2018
Thu gọn, sắp xếp đa thức theo lũy thừa giảm của biến:
* Ta có: f(x) = x7 – 3x2 – x5 + x4 – x2 + 2x – 7
= x7 - (3x2+ x2) – x5+ x4 + 2x – 7
= x7 – 4x2 – x5+ x4 + 2x – 7
= x7 – x5 + x4 – 4x2 + 2x - 7
g(x) = x – 2x2 + x4 – x5 – x7 – 4x2 – 1
= x – ( 2x2 + 4x2) + x4 – x5 –x7 – 1
= x – 6x2 + x4 – x5 – x7 – 1
= -x7 – x5 + x4 – 6x2 + x – 1
* f(x) – g(x)
Vậy f(x) – g(x) = 2x7 + 2x2 + x - 6
PT
1
TN
12 tháng 4 2018
2KClO3--->2KCl+3O2
.. .. .. .. .. ..
O2+ S --->SO2
.. .. .. .. .. .. ..
3O2+2H2S->2SO2+2H2O
.. .. .. .. .. ..
O2+2H2--->2H2O
.. .. .. .. .. ..
O2+2SO2--->2SO3
.. .. .. .. .. ..
SO3+H2O--->H2SO4
NHA..
1
\(4x^4+81\)
\(=\left(2x^2\right)^2+9^2+2.2x^2.9-2.2x^2.9\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2+9-6x\right)\left(2x^2+9+6x\right)\)
2
\(4a^4+b^4\)
\(=\left(2x^2\right)^2+\left(b^2\right)^2+2.2a^2.b^2-2.2a^2.b^2\)
\(=\left(2a^2+b^2\right)^2-\left(2ab\right)^2\)
\(=\left(2a^2+b^2-2ab\right)\left(2a^2+b^2+2ab\right)\)
3
\(x^7+x^5+1\)
\(=\left(x^7-x\right)+\left(x^5-x^2\right)+\left(x^2+x+1\right)\)
\(=x\left(x^6-1\right)+x^2\left(x^3-1\right)+\left(x^2+x+1\right)\)
\(=x\left[\left(x^3\right)^2-1^2\right]+x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=x\left(x^3-1\right)\left(x^3+1\right)+\left(x^2+x+1\right)\left[x^2\left(x-1\right)+1\right]\)
\(=x\left(x-1\right)\left(x^2+x+1\right)\left(x^3+1\right)+\left(x^2+x+1\right)\left[x^2\left(x-1\right)+1\right]\)
\(=\left(x+x+1\right)\left[x\left(x-1\right)\left(x^3+1\right)+x^2\left(x-1\right)+1\right]\)
4
\(x^5+x^4+1\)
\(=\left(x^5+x^4+x^3\right)+x^2+x+1-x^3-x^2-x\)
\(=x^3\left(x^2+x+1\right)+\left(x^2+x+1\right)-x\left(x^2+x+1\right)\)
\(=\left(x^3+1-x\right)\left(x^2+x+1\right)\)