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\(\left(x^3-x^2-5x+21\right):\left(x^2-4x+7\right)\)
\(=\left(x^3-4x^2+3x^2+7x-12x+21\right):\left(x^2-4x+7\right)\)
\(=\left[\left(x^3-4x^2+7x\right)+\left(3x^2-12x+21\right)\right]:\left(x^2-4x+7\right)\)
\(=\left[x\left(x^2-4x+7\right)+3\left(x^2-4x+7\right)\right]:\left(x^2-4x+7\right)\)
\(=\left[\left(x^2-4x+7\right)\left(x+3\right)\right]:\left(x^2-4x+7\right)\)
\(=x+3\)
Bài 4
c) x(x - 2) + (x - 2)²
= (x - 2)(x + x - 2)
= (x - 2)(2x - 2)
= 2(x - 2)(x - 1)
d) 2x(x - y)² - 5(y - x)
= 2x(x - y)² + 5(x - y)
= (x - y)(2x + 5)
Bài 5
a) x² - 6x - 2xy + 12y
= (x² - 6x) - (2xy - 12y)
= x(x - 6) - y(x - 6)
= (x - 6)(x - y)
b) 10ax - 5ay - 2x + y
= (10ax - 5ay) - (2x - y)
= 5a(2x - y) - (2x - y)
= (2x - y)(5a - 1)
c) x⁴ + x³y - x - y
= (x⁴ + x³y) - (x + y)
= x³(x + y) - (x + y)
= (x + y)(x³ - 1)
= (x + y)(x - 1)(x² + x + 1)
d) x³ + 2x² - 4x - 8
= (x³ + 2x²) - (4x + 8)
= x²(x + 2) - 4(x + 2)
= (x + 2)(x² - 4)
= (x + 2)(x + 2)(x - 2)
= (x + 2)²(x - 2)
e) xy - 5x - y² + 5y
= (xy - 5x) - (y² - 5y)
= x(y - 5) - y(y - 5)
= (y - 5)(x - y)
f) ax - bx - 2cx - 2a + 2b + 4c
= (ax - bx - 2cx) - (2a - 2b - 4c)
= x(a - b - 2c) - 2(a - b - 2c)
= (a - b - 2c)(x - 2)
g) 5x²y + 5xy² - b²x - b²y
= (5x²y + 5xy²) - (b²x + b²y)
= 5xy(x + y) - b²(x + y)
= (x + y)(5xy - b²)
h) 4x³ - 4x² - 9x + 9
= (4x³ - 4x²) - (9x - 9)
= 4x²(x - 1) - 9(x - 1)
= (x - 1)(4x² - 9)
= (x - 1)(2x - 3)(2x + 3)
\(\left(x^3-6x^2+9x+14\right):\left(x-7\right)\)
\(=\left(x^3-7x^2+x^2-7x-2x+14\right):\left(x-7\right)\)
\(=[x^2\left(x-7\right)+x\left(x-7\right)-2\left(x-7\right)]:\left(x-7\right)\)
\(=\left(x-7\right)\left(x^2+x-2\right):\left(x-7\right)\)
\(=x^2+x-2\)
a) x2-xy+5y-25
= x(2-y)+ 5(y-2)
= x(2-y)-5(2-y)
= (x-5)(2-y)
g: \(a^3-a^2+9a-9\)
\(=a^2\left(a-1\right)+9\left(a-1\right)\)
\(=\left(a-1\right)\left(a^2+9\right)\)
\(b,=a\left(x+y\right)+2\left(x+y\right)=\left(a+2\right)\left(x+y\right)\\ c,=x\left(x+y\right)-2\left(x+y\right)=\left(x-2\right)\left(x+y\right)\\ d,=5a\left(2x-y\right)-\left(2x-y\right)=\left(5a-1\right)\left(2x-y\right)\)
\(\left(x^2-2x+3\right)\left(\frac{1}{2x}-5\right)\)
\(=\frac{x^2}{2x}-5x^2-\frac{2x}{2x}+10x+\frac{3}{2x}-15\)
\(=\frac{x^2}{2x}-5x^2-16+10x+\frac{3}{2x}\)
\(=-5x^2+\frac{x^2}{2x}+\frac{20x^2}{2x}+\frac{3}{2x}-16\)
\(=-5x^2+\frac{x^2+20x+3}{2x}-16\)
học tốt
(x^2-2x+3)(1/2x-5)=1/2x^3-5x^2-x^2+10x+3/2x-15=1/2x^3-6x^2+11,5x-15
a ) -36a2 + x2 + 4y2 - 4xy
= ( x2 - 4xy + 4y2 ) - (6a)2
= ( x -2y )2 - (6a)2
= ( x - 2y - 6a ).(x - 2y + 6a )
b ) 10ax - 5ay +2x - y
= ( 10ax - 5ay ) + ( 2x - y )
= 5a ( 2x - y ) + ( 2x - y )
= ( 2x - y ) . (5a + 1 )
c ) 2a2b(x + y) - 4ab2(-x - y )
= 2a2b( x+ y ) + 4ab2(x + y )
= 2ab(x + y ) ( a + 2b )
a, \(-36a^2+x^2+4y^2-4xy=\left(x+2y\right)^2-\left(6a\right)^2=\left(x+2y-6a\right)\left(x+2y+6a\right)\)
b, \(10ax-5ay+2x-y=5a\left(2x-y\right)+2x-y=\left(5a+1\right)\left(2x-y\right)\)
c, \(2a^2b\left(x+y\right)-4ab^2\left(-x-y\right)=2a^2b\left(x+y\right)+4ab^2\left(x+y\right)\)
\(=\left(2a^2b+4ab^2\right)\left(x+y\right)=2ab\left(a+2b\right)\left(x+y\right)\)