Phân tích đa thức thành nhân tử:
a) x2 - 3x - 10
b) x4 + 4
K
Khách
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TH
2
23 tháng 8 2021
\(A=x^2+4=\left(x^2+4x+4\right)-4x=\left(x+2\right)^2-\sqrt{4x}=\left(x+2-\sqrt{4x}\right)\left(x+2+\sqrt{4x}\right)\)
\(B=x^4+4y^4=\left(x^4+4x^2y^2+4y^4\right)-4x^2y^2=\left(x^2+2y^2\right)^2-\left(2xy\right)^2=\left(x^2+2y^2-2xy\right)\left(x^2+2y^2+2xy\right)\)
26 tháng 8 2021
a: \(x^4+4=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
b: \(x^8+x^7+1\)
\(=x^8+x^7+x^6-x^6-x^5-x^4+x^5+x^4+x^3-x^3-x^2-x+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)
c: \(x^8+x^4+1\)
\(=\left(x^8+2x^4+1\right)-x^4\)
\(=\left(x^4-x^2+1\right)\cdot\left(x^4+x^2+1\right)\)
\(=\left(x^4-x^2+1\right)\left(x^2+1-x\right)\left(x^2+1+x\right)\)
19 tháng 12 2021
\(a,10x^2y-20xy^2=10xy\left(x-2y\right)\\ b,x^2-y^2+10y-25=x^2-\left(y^2-10y+25\right)=x^2-\left(y-5\right)^2=\left(x-y+5\right)\left(x+y-5\right)\\ c,x^2-y^2+3x-3y=\left(x-y\right)\left(x+y\right)+3\left(x-y\right)=\left(x-y\right)\left(x+y+3\right)\\ d,x^3+3x^2-16x-48=\left(x^3+3x^2\right)-\left(16x+48\right)=x^2\left(x+3\right)-16\left(x+3\right)=\left(x+3\right)\left(x^2-16\right)=\left(x+3\right)\left(x+4\right)\left(x-4\right)\)
\(e,9x^3+6x^2+x=x\left(9x^2+6x+1\right)=x\left(3x+1\right)^2\\ f,x^4+5x^3+15x-9=\left(x^4+5x^3-3x^2\right)+\left(3x^2+15x-9\right)=x^2\left(x^2+5x-3\right)+3\left(x^2+5x-3\right)=\left(x^2+3\right)\left(x^2+5x-3\right)\)
NM
1
1 tháng 10 2021
`a)x^3-8x^2+16x`
`=x(x^2-8x+16)`
`=x(x-4)^2`
`b)x^2+4y^2+2x-4y-4xy-24`
`=(x-2y)^2+2(x-2y)-24`
`=(x-2y)^2-4(x-2y)+6(x-2y)-24`
`=(x-2y-4)(x-2y+6)`
`c)x^4+x^3-x^2-2x-2`
`=x^4-2x^2+x^3-2x+x^2-2`
`=x^2(x^2-2)+x(x^2-2)+x^2-2`
`=(x^2-2)(x^2+x+1)`
NT
3
29 tháng 8 2021
\(A=x^2+3x+2=\left(x+1\right)\left(x+2\right)\)
\(B=x^2-4x-5=\left(x-5\right)\left(x+1\right)\)
\(C=3x^2+7x+4=\left(x+1\right)\left(3x+4\right)\)
29 tháng 8 2021
\(A=x^2+3x+2=\left(x+1\right)\left(x+2\right)\)
\(B=x^2-4x-5=\left(x-5\right)\left(x+1\right)\)
\(C=3x^2+7x+4=\left(x+1\right)\left(3x+4\right)\)
24 tháng 8 2021
\(x^4+4\)
\(=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-4x^2\)
\(=\left(x^2+2x+2\right)\left(x^2-2x+2\right)\)
24 tháng 8 2021
\(A=x^4+4\)
\(=\) \(x^4+4+4x^2-4x^2\)
\(=\left(x^2+2\right)^2-4x^2\)
\(A=\) \(\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)
TP
3
KK
4 tháng 9 2021
c. x2 - 5x + 4
= x2 + x + 4x + 4
= x(x + 1) + 4(x + 1)
= (x + 4)(x + 1)
H9
HT.Phong (9A5)
CTVHS
27 tháng 9 2023
a) \(x^4-y^4\)
\(=\left(x^2\right)^2-\left(y^2\right)^2\)
\(=\left(x^2-y^2\right)\left(x^2+y^2\right)\)
\(=\left(x+y\right)\left(x-y\right)\left(x^2+y^2\right)\)
b) \(x^2-3y^2\)
\(=x^2-\left(y\sqrt{3}\right)^2\)
\(=\left(x-y\sqrt{3}\right)\left(x+y\sqrt{3}\right)\)
c) \(\left(3x-2y\right)^2-\left(2x-3y\right)^2\)
\(=\left(3x-2y+2x-3y\right)\left(3x-2y-3x+2y\right)\)
\(=0\cdot0\)
\(=0\)
d) \(9\left(x-y\right)^2-4\left(x+y\right)^2\)
\(=\left(3x-3y\right)^2-\left(2x+2y\right)^2\)
\(=\left(3x-3y-2x-2y\right)\left(3x-3y+2x+2y\right)\)
\(=\left(x-5y\right)\left(5x-y\right)\)
e) \(\left(4x^2-4x+1\right)-\left(x+1\right)^2\)
\(=\left(2x-1\right)^2-\left(x+1\right)^2\)
\(=\left(2x-1+x+1\right)\left(2x-1-x-1\right)\)
\(=3x\left(x-2\right)\)
f) \(x^3+27\)
\(=x^3+3^3\)
\(=\left(x+3\right)\left(x^2-3x+9\right)\)
g) \(27x^3-0,001\)
\(=\left(3x\right)^3-\left(0,1\right)^3\)
\(=\left(3x-0,1\right)\left(9x^2+0,3x+0,01\right)\)
h) \(125x^3-1\)
\(=\left(5x\right)^3-1^3\)
\(=\left(5x-1\right)\left(25x^2+5x+1\right)\)
H9
HT.Phong (9A5)
CTVHS
27 tháng 9 2023
c) \(\left(3x-2y\right)^2-\left(2x-3y\right)^2\)
\(=\left(3x-2y+2x-3y\right)\left(3x-2y-2x+3y\right)\)
\(=\left(5x-5y\right)\left(x+y\right)\)
\(=5\left(x+y\right)\left(x-y\right)\)
24 tháng 8 2021
a) \(40x^4-10x^2=10x^2\left(4x^2-1\right)=10x^2\left(2x-1\right)\left(2x+1\right)\)
b) \(16x^4-20x^2-y^2-5y=\left(4x^2-\dfrac{5}{2}\right)^2-\left(y-\dfrac{5}{2}\right)^2=\left(4x^2-\dfrac{5}{2}-y+\dfrac{5}{2}\right)\left(4x^2-\dfrac{5}{2}+y-\dfrac{5}{2}\right)=\left(4x^2-y\right)\left(4x^2+y-5\right)\)c)\(64a^2-9b^2-16a+1=\left(8a-1\right)^2-9b^2=\left(8a-1-3b\right)\left(8a-1+3b\right)\)d) \(5x^2+23x-10=5\left(x-\dfrac{2}{5}\right)\left(x+5\right)\)
24 tháng 8 2021
a: \(40x^4-10x^2\)
\(=10x^2\left(4x^2-1\right)\)
\(=10x^2\cdot\left(2x-1\right)\left(2x+1\right)\)
b: \(16x^4-20x^2-y^2-5y\)
\(=\left(4x^2-y\right)\left(4x^2+y\right)-5\left(4x^2+y\right)\)
\(=\left(4x^2+y\right)\left(4x^2-y-5\right)\)
c: Ta có: \(64a^2-9b^2-16a+1\)
\(=\left(8a-1\right)^2-9b^2\)
\(=\left(8a-1-3b\right)\left(8a-1+3b\right)\)
d: Ta có: \(5x^2+23x-10\)
\(=5x^2+25x-2x-10\)
\(=\left(x+5\right)\left(5x-2\right)\)
NM
4
27 tháng 8 2021
b) x2-3x+xy-3y
=\(\left(x^2+xy\right)-\left(3x+3y\right)\)
=\(x\left(x+y\right)-3\left(x+y\right)\)
=\(\left(x-3\right)\left(x+y\right)\)
27 tháng 8 2021
c) x2-y2-4x+4
=(\(x^2-4x+4\))\(-y^2\)
=\(\left(x-2\right)^2\) \(-y^2\)
=(\(x-y-2\)) \(\left(x+y-2\right)\)
b) x^4+4
=(x^2)^2+2^2
=(x^2+2)^2-2x^2.2
=(x^2+2)^2-4x^2
=(x^2+2-2x)(x^2+2+2x)
=(x^2-2x+2)(x^2+2x+2)