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1) \(x^6-x^4-9x^3+9x^2\)
\(=x^2\left(x^4-x^2-9x+9\right)\)
\(=x^2\left[x^2\left(x^2-1\right)-9\left(x-1\right)\right]\)
\(=x^2\left(x-1\right)\left[x^2\left(x+1\right)-9\right]\)
\(=x^2\left(x-1\right)\left(x^3+x^2-9\right)\)
2) \(x^4-4x^3+8x^2-16x+16\)
\(=x^2\left(x^2+4\right)-4x\left(x^2+4\right)+4\left(x^2+4\right)\)
\(=\left(x^2+4\right)\left(x-2\right)^2\)
3) \(x^4-25x^2+20x-4=x^4+5x^3-2x^2-5x^3-25x^2+10x+2x^2+10x-4\)
\(=x^2\left(x^2+5x-2\right)-5x\left(x^2+5x-2\right)+2\left(x^2+5x-2\right)\)
\(=\left(x^2+5x-2\right)\left(x^2-5x+2\right)\)
4) \(5x\left(x-2y\right)+2\left(2y-x\right)^2\)\(=5x\left(x-2y\right)+2\left(x-2y\right)^2=\left(x-2y\right)\left(5x+2x-4y\right)=\left(x-2y\right)\left(7x-4y\right)\)
5) \(x^2\left(x^2-6\right)-x^2+9=x^4-7x^2+9\)
\(=x^4+x^3-3x^2-x^3-x^2+3x-3x^2-3x+9\)
\(=x^2\left(x^2+x-3\right)-x\left(x^2+x-3\right)-3\left(x^2+x-3\right)\)
\(=\left(x^2+x-3\right)\left(x^2-x-3\right)\)
6) \(7x\left(y-4\right)^2-\left(4-y\right)^3=7x\left(y-4\right)^2+\left(y-4\right)^3=\left(y-4\right)^2\left(7x+y-4\right)\)
7) \(x^3+2x^2-6x-27=x^3-3x^2+5x^2-15x+9x-27\)
\(=x^2\left(x-3\right)+5x\left(x-3\right)+9\left(x-3\right)=\left(x-3\right)\left(x^2+5x+9\right)\)
a) Ta có : x2 - 4x + 3
= x2 - x - 3x + 3
= x(x - 1) - (3x - 3)
= x(x - 1) - 3(x - 1)
= (x - 1) (x - 3)
a) \(x^2-4x+3\)
\(=x^2-x-3x+3\)
\(=x\left(x-1\right)-3\left(x-1\right)\)
\(=\left(x-1\right)\left(x-3\right)\)
b) \(x^2+5x+4\)
\(=x^2+x+4x+4\)
\(=x\left(x+1\right)+4\left(x+1\right)\)
\(=\left(x+1\right)\left(x+4\right)\)
c) \(x^2-x-6\)
\(=x^2-3x+2x-6\)
\(=x\left(x-3\right)+2\left(x-3\right)\)
\(=\left(x+2\right)\left(x-3\right)\)
d) \(x^4+1997x^2+1996x+1997\)
\(=x^4+x^2+1996x^2+1996x+1996+1\)
\(=\left(x^4+x^2+1\right)+\left(1996x^2+1996x+1996\right)\)
\(=\left(x^2+x+1\right)\left(x^2-x+1\right)+1996\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2-x+1997\right)\)
e) \(x^2-2001\cdot2002\)( hình như sai sai)
a. x3+5x2+3x-9
= x3-x2+6x2-6x+9x-9
= x2(x-1)+6x(x-1)+9(x-1)
= (x2+6x+9)(x-1)
= (x+3)2(x-1)
b. x3+9x2+11x-21
= x3-x2+10x2-10x+21x-21
= x2(x-1)+10x(x-1)+21(x-1)
= (x2+10x+21)(x-1)
= (x+7)(x+3)(x-1)
c. x3-7x+6
= x3-x2+x2-x-6x+6
= x2(x-1)+x(x-1)-6(x-1)
= (x2+x-6)(x-1)
= (x+3)(x-2)(x-1)
d. x3-5x2+8x-4
= x3-x2-4x2+4x+4x-4
= x2(x-1)-4x(x-1)+4(x-1)
= (x2-4x+4)(x-1)
= (x-2)2(x-1)
e. x3-3x+2
= x3+2x2-2x2-4x+x+2
= x2(x+2)-2x(x+2)+(x+2)
= (x2-2x+1)(x+2)
= (x-1)2(x+2)
f. x3+8x2+17x+10
= x3+5x2+3x2+15x+2x+10
= x2(x+5)+3x(x+5)+2(x+5)
= (x2+3x+2)(x+5)
= (x+1)(x+2)(x+5)
g. x3+3x2+6x+4
= x3+x2+2x2+2x+4x+4
= x2(x+1)+2x(x+1)+4(x+1)
= (x2+2x+4)(x+1)
h. x3-2x-4
= x3-2x2+2x2-4x+2x-4
= x2(x-2)+2x(x-2)+2(x-2)
= (x2+2x+2)(x-2)
k. x3+x2+4
= x3+2x2-x2-2x+2x+4
= x2(x+2)-x(x+2)+2(x+2)
= (x2-x+2)(x+2)
l. x3-12x+7x-2
= x3+2x2-2x2-4x-x-2
= x2(x+2)-2x(x+2)-(x+2)
= (x2-2x-1)(x+2)
a. \(\left(x+y\right)^3+\left(x-y\right)^3\)
\(=x^3+3x^2y+3xy^2+y^3+x^3-3x^2y+3xy^2-y^3\)
\(=2x^3+6xy^2\)
\(=2x\left(x^2+6y^2\right)\)
b. \(x^3-y^3+2x^2-2y^2\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)+2\left(x^2-y^2\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)+2\left(x+y\right)\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2+2x+2y\right)\)
c. \(x^3-y^3-3x^2+3x-1\)
\(=\left(x^3-3x^2+3x-1\right)-y^3\)
\(=\left(x-1\right)^3-y^3\)
\(=\left(x-1-y\right)\left[\left(x-1\right)^2+\left(x-1\right)y+y^2\right]\)
\(=\left(x-y-1\right)\left(x^2+y^2+xy-2x-y+1\right)\)
a ) x3 + 2x - 3
= x3 - x2 + x2 - x + 3x - 3
= x2. ( x - 1 ) + x ( x - 1 ) + 3 . ( x - 1 )
= ( x - 1 ) ( x2 + x + 3 )
b ) x3 - 7x + 6
= x3 - x2 + x2 - x - 6x + 6
= x2 ( x - 1 ) + x ( x - 1 ) - 6 .( x - 1 )
= ( x - 1 ) ( x2 + x - 6 )
= ( x - 1 ) ( x2 - 2x + 3x - 6 )
= ( x - 1 ) [ x ( x - 2 ) + 3. ( x - 2 ) ]
= ( x - 1 ) ( x - 2 ) . ( x + 3 )
c ) x3 + 5x2 + 8x + 4
= x3 + x2 + 4x2 + 4x + 4x + 4
= x2 ( x + 1 ) + 4x ( x + 1 ) + 4 ( x + 1 )
= ( x + 1 ) . ( x2 + 4x + 4 )
= ( x + 1 ) . ( x + 2 )2
d ) x3 - 9x2 + 6x + 16
= x3 + x2 - 10x2 - 10x + 16x + 16
= x2 ( x + 1 ) - 10x ( x + 1 ) + 16 ( x + 1 )
= ( x + 1 ) ( x2 - 10x + 16 )
= ( x + 1 ) ( x2 - 2x - 8x + 16 )
= ( x + 1 ) . [ x. ( x - 2 ) - 8 . ( x - 2 ) ]
= ( x + 1 ) . ( x - 2 ) . ( x - 8 )
e ) x3 - x2 - x - 2
= x3 - 2x2 + x2 - 2x + x - 2
= x2 ( x - 2 ) + x ( x - 2 ) + ( x - 2 )
= ( x - 2 ) ( x2 + x + 1 )
g ) x3 + x2 - x + 2
= x3 + 2x2 - x2 - 2x + x + 2
= x2 ( x + 2 ) - x ( x + 2 ) + ( x + 2 )
= ( x + 2 ) ( x2 - x + 1 )
h ) x3 - 6x2 - x + 30
= x3 + 2x2 - 8x2 - 16x + 15x + 30
= x2 ( x + 2 ) - 8x ( x + 2 ) + 15 ( x + 2 )
= ( x + 2 ) ( x2 - 8x + 15 )
= ( x + 2 ) ( x2 - 5x - 3x + 15 )
= ( x + 2 ) [ x ( x - 5 ) - 3 ( x - 5 ) ]
= ( x + 2 ) ( x - 5 ) ( x - 3 )
a ) x3 + 2x - 3
= x3 - x2 + x2 - x + 3x - 3
= x2. ( x - 1 ) + x ( x - 1 ) + 3 . ( x - 1 )
= ( x - 1 ) ( x2 + x + 3 )
b ) x3 - 7x + 6
= x3 - x2 + x2 - x - 6x + 6
= x2 ( x - 1 ) + x ( x - 1 ) - 6 .( x - 1 )
= ( x - 1 ) ( x2 + x - 6 )
= ( x - 1 ) ( x2 - 2x + 3x - 6 )
= ( x - 1 ) [ x ( x - 2 ) + 3. ( x - 2 ) ]
= ( x - 1 ) ( x - 2 ) . ( x + 3 )
P/s tham khảo nha