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a) \(3x^2-9x+30=3\left(x^2-3x+10\right)\)
b) \(3x^2-5x-2=3x^2-6x+x-2\)
\(=3x\left(x-2\right)+\left(x-2\right)=\left(3x+1\right)\left(x-2\right)\)
c) \(x^4+4y^4\)
\(=x^4+4y^4+2x^2y^2+2x^2y^2-4x^2y^2+4xy^3-4xy^3+2x^3y-2x^3y\)
\(=\left(4y^4-4xy^3+2x^2y^2\right)+\left(4xy^3-4x^2y^2+2x^3y\right)\)
\(+\left(2x^2y^2-2x^3y+x^4\right)\)
\(=2y^2\left(2y^2-2xy+x^2\right)+2xy\left(2y^2-2xy+x^2\right)\)
\(+x^2\left(2y^2-2xy+x^2\right)\)
\(=\left(2y^2+2xy+x^2\right)\left(2y^2-2xy+x^2\right)\)
d) \(x^5+x+1\)
\(=x^5+x+1+x^4-x^4+x^3-x^3+x^2-x^2\)
\(=\left(x^5-x^4+x^2\right)+\left(x^4-x^3+x\right)+\left(x^3-x^2+1\right)\)
\(=x^2\left(x^3-x^2+1\right)+x\left(x^3-x^2+1\right)+\left(x^3-x^2+1\right)\)
\(=\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)
a ) \(x^3-3x^2-4x+12\)
\(=x^2\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x^2-4\right)\left(x-3\right)\)
\(=\left(x-3\right)\left(x-2\right)\left(x+2\right)\)
b ) \(x^4-5x^2+4\)
\(=x^4-4x^2-x^2+4\)
\(=x^2\left(x^2-4\right)-\left(x^2-4\right)\)
\(\Leftrightarrow\left(x^2-1\right)\left(x^2-4\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)\)
\(=\left(x-2\right)\left(x-1\right)\left(x+1\right)\left(x+2\right)\)
Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
a) \(x^2yz+4zyx+4yz\)
\(=yz\left(x^2+4x+4\right)\)
\(=yz\left(x+2\right)^2\)
b) \(5x^4-3x^3y-45x^2y^2+27xy^3\)
\(=x\left(5x^3-3x^2y-45xy^2+27y^3\right)\)
a, 8x2+10x =2x.(4x+5)
b, 4x2-8x+4 =4.(x2 -2x+1)=4.(x-1)2
c, 3x2 -3xy -5x +5y =(3x2-5x) - (3xy-5y) = x.(3x-5)- y.(3x-5)= (x-y).(3x-5)
d, x2+ 4x- 45=x2+ 9x- 5x- 45= x.(x+9)- 5.(x+9)=(x-5).(x+9)
a , 8 x 2 + 10 x
= 2 x ( 4 x + 5 )
b , 4 x 2 - 8 x + 4
= ( 2x ) 2 - 2 . 2 x . 2 + 2 2
= ( 2x + 2 ) 2
c ) 3 x 2 - 3 x y - 5 x + 5 y
= 3 x ( x - y ) - 5 ( x - y )
= ( 3x - 5 ) ( x - y )
d ) x 2 + 4x - 45
= x 2 + 2 x . 2 + 4 - 49
= ( x + 2 ) 2 - 49
= ( x + 2 ) 2 - 7 2
= ( x + 2 - 7 ) ( x + 2 + 7)
= ( x - 5 ) ( x + 9 )
a) x^3−3x^2−4x+12
=(x^3-3x^2)-(4x-12)
=x^2(x-3)-4(x-3)
=(x-3)(x^2-4)=(x-3)(x-2)(x+2)
b) x^4-5x^2+4=x^4-x^2-4x^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)
c) (x+y+z)^3-x^3-y^3-z^3
=x^3+y^3+z^3+3x^2yz+3xy^2z+3xyz^2-x^3-y^3-z^3
=3x^2yz+3xy^2z+3xyz^2
3xyz(x+y+z)
Bài làm:
a) \(x^2-6x+4=\left(x^2-6x+9\right)-5=\left(x-3\right)^2-\left(\sqrt{5}\right)^2\)
\(=\left(x-3-\sqrt{5}\right)\left(x-3+\sqrt{5}\right)\)
b) \(x^2-4x+3=x^2-x-3x+3=\left(x-1\right)\left(x-3\right)\)
c) \(6x^2-5x+1=6x^2-3x-2x+1=\left(2x-1\right)\left(3x-1\right)\)
d) \(3x^2+13x-10=3x^2+15x-2x-10=\left(x-5\right)\left(3x-2\right)\)
Mình xin lỗi nhé, để mình sửa lại : ^^
a) \(x^4+3x^2+4=\left(x^4+x^3+2x^2\right)+-\left(x^3+x^2+2x\right)+2\left(x^2+2x+2\right)\)
\(=x^2\left(x^2+x+2\right)-x\left(x^2+x+2\right)+2\left(x^2+x+2\right)=\left(x^2-x+2\right)\left(x^2+x+2\right)\)
b) \(x^4+5x^2+9=\left(x^4+x^3+3x^2\right)-\left(x^3+x^2+3x\right)+3\left(x^2+x+3\right)\)
\(=x^2\left(x^2+x+3\right)-x\left(x^2+x+3\right)+3\left(x^2+x+3\right)=\left(x^2-x+3\right)\left(x^2+x+3\right)\)