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3 tháng 8 2018
Câu a : \(4x^3-5x^2+6x+9\)
\(=4x^3+3x^2-8x^2-6x+12x+9\)
\(=\left(4x^3+3x^2\right)-\left(8x^2+6x\right)+\left(12x+9\right)\)
\(=x^2\left(4x+3\right)-2x\left(4x+3\right)+3\left(4x+3\right)\)
\(=\left(4x+3\right)\left(x^2-2x+3\right)\)
Câu b : \(5x^3-12x^2+14x-4\)
\(=5x^3-10x^2-2x^2+10x+4x-4\)
\(=\left(5x^3-2x^2\right)-\left(10x^2-4x\right)+\left(10x-4\right)\)
\(=x^2\left(5x-2\right)-2x\left(5x-2\right)+2\left(5x-2\right)\)
\(=\left(5x-2\right)\left(x^2-2x+2\right)\)
Câu c : \(x^3-5x^2+2x+8\)
\(=x^3+x^2-6x^2-6x+8x+8\)
\(=\left(x^3+x^2\right)-\left(6x^2+6x\right)+\left(8x+8\right)\)
\(=x^2\left(x+1\right)-6x\left(x+1\right)+8\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-6x+8\right)\)
\(=\left(x+1\right)\left[x^2-2x-4x+8\right]\)
\(=\left(x+1\right)\left[x\left(x-2\right)-4\left(x-2\right)\right]\)
\(=\left(x+1\right)\left(x-2\right)\left(x-4\right)\)
Câu d : \(4x^3+5x^2+10x-12\)
\(=4x^3+8x^2-3x^2+16x-6x-12\)
\(=\left(4x^3-3x^2\right)+\left(8x^2-6x\right)+\left(16x-12\right)\)
\(=x^2\left(4x-3\right)+2x\left(4x-3\right)+4\left(4x-3\right)\)
\(=\left(4x-3\right)\left(x^2+2x+4\right)\)
MD
2
DN
21 tháng 12 2023
`#3107`
`a.`
`4x^2 - 6x = 2x(2x - 3)`
`b.`
`9x^4y^3 + 3x^2y^4 = 3x^2y^2(3x^2y + y^2)`
`c.`
`x^3 - 2x^2 + 5x`
`= x(x^2 - 2x + 5)`
KV
21 tháng 12 2023
a) 4x² - 6x
= 2x(2x - 3)
b) 9x⁴y³ + 3x²y⁴
= 3x²y³(3x² + 3y)
c) x³ - 2x² + 5x
= x(x² - 2x + 5)
30 tháng 7 2021
1, \(x^2\left(x-3\right)-4x+12=x^2\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x-2\right)\left(x+2\right)\left(x-3\right)\)
2, \(2a\left(x+y\right)-x-y=2a\left(x+y\right)-\left(x+y\right)=\left(2a-1\right)\left(x+y\right)\)
3, \(2x-4+5x^2-10x=2\left(x-2\right)+5x\left(x-2\right)=\left(2+5x\right)\left(x-2\right)\)
4, sửa đề :
\(6x^2-12x-7x+14=6x\left(x-2\right)-7\left(x-2\right)=\left(6x-7\right)\left(x-2\right)\)
5, \(xy-y^2-3x+3y=y\left(x-y\right)-3\left(x-y\right)=\left(y-3\right)\left(x-y\right)\)
AD
30 tháng 7 2021
a) x2(x-3)-4x+12
=x2(x-3)-4(x-3)
=(x-3)(x2-4)
=(x-3)(x-2)(x+2)
b) 2a(x+y)-x-y
=2a(x+y)-(x+y)
=(x+y)(2a-1)
c) 2x-4+5x2-10x
=2(x-2)+5x(x-2)
=(x-2)(2+5x)
d) 5x2-12x-7x+14
=5x2-19x+14
e) xy-y2-3x+3y
=y(x-y)-3(x-y)
=(x-y)(y-3)
#H
18 tháng 8 2021
\(A=\left(5x^5+5x^4\right):5x^2-\left(2x^4-8x^2-6x+12\right):\left(2x-4\right)\)
Phép chia thứ nhất:
\(\left(5x^5+5x^4\right):5x^2=x^3+x^2\)
Phép chia thứ hai:
Vậy A = ( x^3 + x^2 ) - ( x^3 + 2x^2 - 3 ) = -x^2 + 3
Với x = -2 thì: A = -(-2)^2 + 3 = -4 + 3 = -1
B) bạn làm tương tự nhé
24 tháng 12 2020
Bài 1:
a) Ta có: \(\left(15x^2\cdot y^2\cdot z\right):3xyz\)
\(=\dfrac{15x^2y^2z}{3xyz}\)
\(=5xy\)
b) Ta có: \(3x^2\cdot\left(5x^2-4x+3\right)\)
\(=3x^2\cdot5x^2-3x^2\cdot4x+3x^2\cdot3\)
\(=15x^4-12x^3+9x^2\)
c) Ta có: \(\left(2x^2-3x\right):\left(x-4\right)\)
\(=\dfrac{2x^2-8x+5x-20+20}{x-4}\)
\(=\dfrac{2x\left(x-4\right)+5\left(x-4\right)+20}{x-4}\)
\(=2x+5+\dfrac{20}{x-4}\)
d) Ta có: \(-5xy\cdot\left(3x^2y-5xy+y^2\right)\)
\(=-5xy\cdot3x^2y+5xy\cdot5xy-5xy\cdot y^2\)
\(=-15x^3y^2+25x^2y^2-5xy^3\)
5 tháng 8 2021
a)x²−2x−4y²−4ya)x²-2x-4y²-4y
=x²−2x−4y²−4y+2xy−2xy=x²-2x-4y²-4y+2xy-2xy
=(x²−2xy−2x)+(2xy−4y²−4y)=(x²-2xy-2x)+(2xy-4y²-4y)
=x(x−2y−2)+2y(x−2y−2)=x(x-2y-2)+2y(x-2y-2)
=(x+2y)(x−2y−2)=(x+2y)(x-2y-2)
b)x4+2x³−4x−4b)x4+2x³-4x-4
=x4+2x³+2x²−2x²−4x−4=x4+2x³+2x²-2x²-4x-4
=(x4+2x³+2x²)−(2x²+4x+4)=(x4+2x³+2x²)-(2x²+4x+4)
=x²(x²+2x+2)−2(x²+2x+2)=x²(x²+2x+2)-2(x²+2x+2)
=(x²−2)(x²+2x+2)=(x²-2)(x²+2x+2)
c)x³+2x²y−x−2yc)x³+2x²y-x-2y
=x²(x+2y)−(x+2y)=x²(x+2y)-(x+2y)
=(x²−1)(x+2y)=(x²-1)(x+2y)
=(x+1)(x−1)(x+2y)=(x+1)(x-1)(x+2y)
d)3x²−3y²−2(x−y)²d)3x²-3y²-2(x-y)²
=3(x²−y²)−2(x−y)²=3(x²-y²)-2(x-y)²
=3(x+y)(x−y)−2(x−y)²=3(x+y)(x-y)-2(x-y)²
=(x−y)[3(x+y)−2(x−y)]=(x-y)[3(x+y)-2(x-y)]
=(x−y)(3x+3y−2x+2y)=(x-y)(3x+3y-2x+2y)
=(x−y)(x+5y)=(x-y)(x+5y)
e)x³−4x²−9x+36e)x³-4x²-9x+36
=(x³−4x²)−(9x−36)=(x³-4x²)-(9x-36)
=x²(x−4)−9(x−4)=x²(x-4)-9(x-4)
=(x−4)(x²−9)=(x-4)(x²-9)
=(x−4)(x²−3²)=(x-4)(x²-3²)
=(x−4)(x+3)(x−3)=(x-4)(x+3)(x-3)
f)x²−y²−2x−2yf)x²-y²-2x-2y
=(x²−y²)−(2x+2y)=(x²-y²)-(2x+2y)
=(x+y)(x−y)−2(x+y)=(x+y)(x-y)-2(x+y)
=(x+y)(x−y−2)
hok tốt nhé
k đi
x4 + 2x3 + 5x2 + 4x - 12
= x4 + x3 + x3 + 6x2 + x2 - 2x2 + 6x - 2x - 12
= ( x4 + x3 + 6x2 ) + ( x3 + x2 + 6x ) - ( 2x2 + 2x + 12 )
= x2( x2 + x + 6 ) + x( x2 + x + 6 ) - 2( x2 + x + 6 )
= ( x2 + x + 6 )( x2 + x - 2 )
= ( x2 + x + 6 )( x2 - x + 2x - 2 )
= ( x2 + x + 6 )[ x( x - 1 ) + 2( x - 1 ) ]
= ( x2 + x + 6 )( x - 1 )( x + 2 )