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MK
7
1 tháng 3 2015
x8 + 14x4 + 1
= [(x4)2 + 2.7.x2 + 49] - 48
=(x4 + 7)2 - (\(\sqrt{48}\))2
=(x4 + 7 + căn482).(x4 + 7 - căn482)
NT
3
B
16 tháng 11 2018
a, \(x^3-x^2-4\)
\(=x^3-2x^2+x^2-2x+2x-4\)
\(=x^2\left(x-2\right)+x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+x+2\right)\)
16 tháng 11 2018
a) \(x^3-x^2-4\)
\(=x^3-2x^2+x^2-2x+2x-4\)
\(=x^2\left(x-2\right)+x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+x+2\right)\)
b) \(x^8-98x^4+1\)
\(=\left(x^4\right)^2+2\cdot x^4\cdot1+1^2-100x^4\)
\(=\left(x^4+1\right)^2-\left(10x^2\right)^2\)
\(=\left(x^4-10x^2+1\right)\left(x^4+10x^2+1\right)\)
PT
1
TN
16 tháng 6 2017
a)\(3x^2-8x+4\)
\(=3x^2-2x-6x+4\)
\(=x\left(3x-2\right)-2\left(3x-2\right)\)
\(=\left(x-2\right)\left(3x-2\right)\)
b)\(4x^4+81\)
\(=4x^4+36x^2+81-36x^2\)
\(=\left(2x^2+9\right)^2-36x^2\)
\(=\left(2x^2-6x+9\right)\left(2x^2+6x+9\right)\)
c)\(x^8+98x^4+1\)
\(=\left(x^8+2x^4+1\right)+96x^4\)
\(=\left(x^4+1\right)^2+16x^2\left(x^4+1\right)+64x^4-16x^2\left(x^4+1\right)+32x^4\)
\(=\left(x^4+8x^2+1\right)^2-16x^2\left(x^4-2x^2+1\right)\)
\(=\left(x^4+8x^2+1\right)^2-16x^2\left(x^4-2x^2+1\right)\)
\(=\left(x^4+8x^2+1\right)^2-\left(4x^3-4x\right)^2\)
\(=\left(x^4+4x^3+8x^2-4x+1\right)\left(x^4-4x^3+8x^2+4x+1\right)\)
d)\(x^4+6x^3+7x^2-6x+1\)
\(=x^4+3x^3-x^2+3x^3+9x^2-3x-x^2-3x+1\)
\(=x^2\left(x^2+3x-1\right)+3x\left(x^2+3x-1\right)-\left(x^2+3x-1\right)\)
\(=\left(x^2+3x-1\right)\left(x^2+3x-1\right)\)\(=\left(x^2+3x-1\right)^2\)
A
2
AH
Akai Haruma
Giáo viên
15 tháng 10 2020
Lời giải:
a)
$x^8+98x^4+1=(x^4+1)^2+96x^4=(x^4+1)^2+(8x^2)^2+16x^2(x^4+1)+32x^4-16x^2(x^4+1)$
$=(x^4+1+8x^2)^2-16x^2(x^4+1-2x^2)$
$=(x^4+1+8x^2)^2-16x^2(x^2-1)^2$
$=(x^4+1+8x^2)^2-[4x(x^2-1)]^2=(x^4+1+8x^2-4x^3+4x)(x^4+4x^3+8x^2-4x+1)$
b)
$(x^2+2x)(x^2+2x+4)+3$
$=(x^2+2x)^2+4(x^2+2x)+3$
$=(x^2+2x)^2+(x^2+2x)+3(x^2+2x)+3$
$=(x^2+2x)(x^2+2x+1)+3(x^2+2x+1)$
$=(x^2+2x+3)(x^2+2x+1)=(x^2+2x+3)(x+1)^2$
17 tháng 8 2020
Lời giải:
a)
$x^8+98x^4+1=(x^4+1)^2+96x^4=(x^4+1)^2+(8x^2)^2+16x^2(x^4+1)+32x^4-16x^2(x^4+1)$
$=(x^4+1+8x^2)^2-16x^2(x^4+1-2x^2)$
$=(x^4+1+8x^2)^2-16x^2(x^2-1)^2$
$=(x^4+1+8x^2)^2-[4x(x^2-1)]^2=(x^4+1+8x^2-4x^3+4x)(x^4+4x^3+8x^2-4x+1)$
b)
$(x^2+2x)(x^2+2x+4)+3$
$=(x^2+2x)^2+4(x^2+2x)+3$
$=(x^2+2x)^2+(x^2+2x)+3(x^2+2x)+3$
$=(x^2+2x)(x^2+2x+1)+3(x^2+2x+1)$
$=(x^2+2x+3)(x^2+2x+1)=(x^2+2x+3)(x+1)^2$
20 tháng 7 2018
a) \(x^3+3x^2y-9xy^2+5y^3\)
\(=x^3-3x^2y+3xy^2-y^3+6x^2y-12xy^2+6y^3\)
\(=\left(x-y\right)^3+6y\left(x^2-2xy+y^2\right)\)
\(=\left(x-y\right)^3+6y\left(x-y\right)^2\)
\(=\left(x-y\right)^2\left(x+5y\right)\)
20 tháng 7 2018
b) \(27x^3-27x^2+18x-4\)
\(=27x^3-9x^2-18x^2+6x+12x-4\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)\)
\(=\left(3x-1\right)\left(9x^2-6x+4\right)\)
c) \(2x^3-x^2+5x+3\)
\(=2x^3+x^2-2x^2-x+6x+3\)
\(=x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
DT
2
2 tháng 9 2017
b) 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).[(x2-x).(x3 +1) + 1]
= (x2 + x +1).(x5-x4 + x2 -x + 1
2 tháng 9 2017
\(h\left(x\right)=x^7+x^5+1=x^7+x^6+x^5-x^6+1=x^5\left(x^2+x+1\right)-\left(x^3+1\right)\left(x^3-1\right)\)
\(=x^5\left(x^2+x+1\right)-\left(x^3+1\right)\left(x-1\right)\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^5-x^4+x^3-x+1\right)\)
a) \(x^8+14x^4+1=\left(x^4+1\right)^2+12x^4=\left(x^4+1\right)^2+4x^2\left(x^4+1\right)+4x^4-4x^2\left(x^4+1\right)+8x^4\)
\(=\left(x^4+2x^2+1\right)^2-4x^2\left(x^4-2x^2+1\right)=\left(x^4+2x^2+1\right)^2-\left(2x\left(x^2-1\right)\right)^2\)
\(=\left(x^4-2x^3+2x^2+2x+1\right)\left(x^4+2x^3+2x^2-2x+1\right)\)