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20 tháng 12 2020
1, \(45+x^3-5x^2-9x=9\left(5-x\right)+x^2\left(x-5\right)\)
\(=\left(9-x^2\right)\left(x-5\right)=\left(3-x\right)\left(x+3\right)\left(x-5\right)\)
3, \(x^4-5x^2+4\)
Đặt \(x^2=t\left(t\ge0\right)\)ta có :
\(t^2-5t+4=t^2-t-4t+4=t\left(t-1\right)-4\left(t-1\right)\)
\(=\left(t-4\right)\left(t-1\right)=\left(x^2-4\right)\left(x^2-1\right)=\left(x-2\right)\left(x+2\right)\left(x-1\right)\left(x+1\right)\)
YN
29 tháng 3 2022
`Answer:`
1. `45+x^3-5x^2-9x`
`=x^3+3x^2-8x^2-24x+15x+45x`
`=x^2 .(x+3)-8x.(x+3)+15.(x+3)`
`=(x+3).(x^2-8x+15)`
`=(x+3).(x^2-5x-3x+15)`
`=(x-3).(x-5).(x-3)`
2. `x^4-2x^3-2x^2-2x-3`
`=x^4+x^3-3x^3+x^2+x-3x-3`
`=x^3 .(x+1)-3x^2 .(x+1)+x.(x+1)-3.(x+1)`
`=(x+1).(x^3-3x^2+x-3)`
`=(x+1).[x^3 .(x-3).(x-3)]`
`=(x+1).(x-3).(x^2+1)`
3. `x^4-5x^2+4`
`=x^4-x^2-4x^2+4`
`=x^2 .(x^2-1)-4.(x^2-1)`
`=(x^2-1).(x^2-4)`
`=(x-1).(x+1).(x-2).(x+2)`
4. `x^4+64`
`=x^4+16x^2+64-16x^2`
`=(x^2+8)^2-16x^2`
`=(x^2+8-4x).(x^2+8+4x)`
5. `x^5+x^4+1`
`=x^5+x^4+x^3-x^3+1`
`=x^3 .(x^2+x+1)-(x^3-1)`
`=x^3 .(x^2+x+1)-(x-1).(x^2+x+1)`
`=(x^2+x+1).(x^3-x+1)`
6. `(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+1).(x^2+2x)+3.(x^2+2x+1)`
`=(x^2+2x+1).(x^2+2x+3)`
`=(x+1)^2 .(x^2+2x+3)`
7. `(x^3+4x+8)^2+3x.(x^2+4x+8)+2x^2`
`=x^6+8x^4+16x^3+16x^2+64x+64+3x^3+12x^2+24x+2x^2`
`=x^6+8x^4+19x^3+30x^2+88x+64`
8. `x^3 .(x^2-7)^2-36x`
`=x[x^2.(x^2-7)^2-36]`
`=x[(x^3-7x)^2-6^2]`
`=x.(x^3-7x-6).(x^3-7x+6)`
`=x.(x^3-6x-x-6).(x^3-x-6x+6)`
`=x.[x.(x^2-1)-6.(x+1)].[x.(x^2-1)-6.(x-1)]`
`=x.(x+1).[x.(x-1)-6].(x-1).[x.(x+1)-6]`
`=x.(x+1).(x-1).(x^2-3x+2x-6).(x^2+3x-2x-6)`
`=x.(x+1).(x-1).[x.(x-3)+2.(x-3)].[x.(x+3)-2.(x+3)]`
`=x.(x+1)(x-1).(x-2).(x+2).(x-3).(x+3)`
9. `x^5+x+1`
`=x^5-x^2+x^2+x+1`
`=x^2 .(x^3-1)+(x^2+x+1)`
`=x^2 .(x-1).(x^2+x+1)+(x^2+x+1)`
`=(x^2+x+1).(x^3-x^2+1)`
10. `x^8+x^4+1`
`=[(x^4)^2+2x^4+1]-x^4`
`=(x^4+1)^2-(x^2)^2`
`=(x^4-x^2+1).(x^4+x^2+1)`
`=[(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-x+1).(x^2+x+1).(x^4-x^2+1)
11. ` x^5-x^4-x^3-x^2-x-2`
`=x^5-2x^4+x^4-2x^3+x^3-2x^2+x^2-2x+x-2`
`=x^4 .(x-2)+x^3 ,(x-2)+x^2 .(x-2)+x.(x-2)+(x-2)`
`=(x-2).(x^4+x^3+x^2+x+1)`
12. `x^9-x^7-x^6-x^5+x^4+x^3+x^2-1`
`=(x^9-x^7)-(x^6-x^4)-(x^5-x^3)+(x^2-1)`
`=x^7 .(x^2-1)-x^4 .(x^2-1)-x^3 .(x^2-1)+(x^2-1)`
`=(x^2-1).(x^7-x^4-x^3+1)`
`=(x-1)(x+1)(x^3-1)(x^4-1)`
`=(x-1)(x+1)(x^2+x+1)(x-1)(x^2-1)(x^2+1)`
`=(x-1)^2 .(x+1)(x^2+x+1)(x-1)(x+1)(x^2+1)`
`=(x-1)^3 .(x+1)^2 .(x^2+x+1)(x^2+1)`
13. `(x^2-x)^2-12(x^2-x)+24`
`=[ (x^2-x)^2-2.6(x^2-x)+6^2]-12`
`=(x^2-x+6)^2-12`
`=(x^2-x+6-\sqrt{12})(x^2-x+6+\sqrt{12})`
22 tháng 9 2020
a) ( x + 2 )( x + 3 ) - ( x - 2 )( x + 5 )
= x2 + 5x + 6 - ( x2 + 3x - 10 )
= x2 + 5x + 6 - x2 - 3x + 10
= 2x + 16
b) ( 8 - 5x )( x + 2 ) + 4( x - 2 )( x + 1 ) + 2( x - 2 )( x + 2 ) + 10
= -5x2 - 2x + 16 + 4( x2 - x - 2 ) + 2( x2 - 4 ) + 10
= -5x2 - 2x + 16 + 4x2 - 4x - 8 + 2x2 - 8 + 10
= x2 - 6x + 10
c) 4( x - 1 )( x + 5 ) - ( x + 2 )( x + 5 ) - 3( x - 1 )( x + 2 )
= 4( x2 + 4x - 5 ) - ( x2 + 7x + 10 ) - 3( x2 + x - 2 )
= 4x2 + 16x - 20 - x2 - 7x - 10 - 3x2 - 3x + 6
= 6x - 24
d) ( x - 1 )( x5 + x4 + x3 + x2 + x + 1 )
= x6 + x5 + x4 + x3 + x2 + x - x5 - x4 - x3 - x2 - x - 1
= x6 - 1
2 tháng 10 2020
a) 2x( x - 7 ) - ( x + 3 )( x - 2 ) - ( x + 4 )( x - 4 )
= 2x2 - 14x - ( x2 + x - 6 ) - ( x2 - 16 )
= 2x2 - 14x - x2 - x + 6 - x2 + 16
= 22 - 15x
b) ( 2x + 5 )( x - 2 ) - 3( x + 2 )2 + ( x + 1 )2
= 2x2 + x - 10 - 3( x2 + 4x + 4 ) + x2 + 2x + 1
= 3x2 + 3x - 9 - 3x2 - 12x - 12
= -9x - 21
c) ( x + 3 )( x - 3 ) - ( x + 5 )( x - 1 ) - ( x - 4 )2
= x2 - 9 - ( x2 + 4x - 5 ) - ( x2 - 8x + 16 )
= x2 - 9 - x2 - 4x + 5 - x2 + 8x - 16
= -x2 + 4x - 20
d) 2x( x + 1 )2 - ( x - 1 )3 - ( x - 2 )( x2 + 2x + 4 )
= 2x( x2 + 2x + 1 ) - ( x3 - 3x2 + 3x - 1 ) - ( x3 - 8 )
= 2x3 + 4x2 + 2x - x3 + 3x2 - 3x + 1 - x3 + 8
= 7x2 - x + 9
e) ( x + 5 )( x - 5 )( x + 2 ) - ( x + 2 )3
= ( x2 - 25 )( x + 2 ) - ( x3 + 6x2 + 12x + 8 )
= x3 + 2x2 - 25x - 50 - x3 - 6x2 - 12x - 8
= -4x2 - 37x - 58
17 tháng 3 2020
a) (x-3)2- 4(x-5)= (4-x)2
<=> x2- 6x+ 9- 4x+ 20= 16- 8x+ x2
<=> x2- x2- 6x- 4x+ 8x= 16- 9- 20
<=> -2x = -13
<=> x = \(\frac{13}{2}\)
b) 3(x-2)(x+2) = (2x-1)2-(x-3)2
<=> 3(x2-4) = 4x2- 4x +1 - (x2-6x +9)
<=> 3x2 - 12 = 4x2 - 4x + 1 - x2 +6x - 9
<=> 3x2 - 12 = 3x2 + 2x - 8
<=> 3x2 -3x2 - 2x = 12 - 8
<=> -2x = 4
<=> x = -2
c) ( x + 4)2- (x-5)2 = 5(x - 4)
<=> x2+ 8x +16 - ( x2-10x +25) = 5x - 20
<=> x2+ 8x +16 - x2 +10x -25 = 5x - 20
<=> 18x - 9 - 5x + 20 = 0
<=> 13x + 11 = 0
<=> 13x = -11
<=> x = \(\frac{-11}{13}\)
d) x(3+x)2 - 1 = (x+2)3
<=> x( 9 + 6x + x2 ) - 1 = x3 + 6x2 + 12x + 8
<=> 9x + 6x2 + x3 - 1 - x3 - 6x2 - 12x - 8 = 0
<=> -3x - 9 = 0
<=> -3x = 9
<=> x = -3
HY
6 tháng 2 2020
\(a.-3x\left(x+2\right)^2+\left(x+3\right)\left(x-1\right)\left(x+1\right)-\left(2x-5\right)^2\\ =-3x\left(x^2+4x+4\right)+\left(x+3\right)\left(x^2-1\right)-\left(4x^2-20x+25\right)\\ =-3x^3-12x^2-12x+x^3-x+3x^2-3-4x^2+20x-25\\ =-3x^3+x^3-12x^2+3x^2-4x^2-12x-x+20x-3-25\\ =-2x^3-13x^2+7x-28\\ \)\(b.2\left(x-3\right)\left(x+3\right)\left(x+2\right)-\left(x-1\right)\left(x^2-3\right)-5x\left(x+4\right)^2-\left(x-5\right)^2\\ =2\left(x^2-9\right)\left(x+2\right)-\left(x^3-3x-x^2+3\right)-5x\left(x^2+8x+16\right)-\left(x^2-10x+25\right)\\ =2\left(x^3+2x^2-9x-18\right)-x^3+3x+x^2-3-5x^3-40x^2-80x-x^2+10x-25\\ =2x^3+4x^2-18x-36-x^3+3x+x^2-3-5x^3-40x^2-80x-x^2+10x-25\\ =2x^3-x^3-5x^3+4x^2+x^2-40x^2-x^2-18x+3x-80x+10x-36-3-25\\ =-4x^3-36x^2-85x-64\)
13 tháng 6 2018
1/ (x+1)(-3)+5(x-4)=-3
\(\Leftrightarrow\)-3x - 3 + 5x - 20= -3
\(\Leftrightarrow\)2x - 23=-3
\(\Leftrightarrow\)x=10
2/3(5x-1) -x (x+1)+x2=14
\(\Leftrightarrow\)15x - 3 - x2 -x + x2=14
\(\Leftrightarrow\)14x=17
\(\Leftrightarrow\)x=17/14
3/2(x-1)-x(3-x)=x2
\(\Leftrightarrow\)2x - 2 - 3x + x2=x2
\(\Leftrightarrow\)2x-3x+x2-x2=2
\(\Leftrightarrow\)x= -2
4/ 3x(x+5)-2(x+5)=3x2
\(\Leftrightarrow\)3x2 + 15x - 2x - 10=3x2
\(\Leftrightarrow\)13x = 10
\(\Leftrightarrow\)x=10/13
5/ 4x(x+2)+x(4-x)=3x2+12
\(\Leftrightarrow\)4x2 + 8x + 4x - x2 = 3x2 + 12
\(\Leftrightarrow\)12x=12
\(\Leftrightarrow\)x=1
\(\left(x^5-1\right)-\left(x^4+x^3+x^2+x+1\right)=\left(x^4+..+1\right)\left(x-2\right)\)