Question

1/ phân tích đa thức thành nhân tử:

a) x³-x+3x²y+3xy²+y³-y

c) 5x²-10xy+5y²-20z²
2/ Tìm x, biết:

a) 5x(x-1)=x-1            b) 2(x+5)-x²-5x=0

Answer 1

1/a ) = (x+y)³ -(x+y)

= (x+y)[(x+y)²+1]

c) = 5(x²-xy+y²)-20z²

=5(x-y)²-20z²

= 5 [ (x-y)²- 4z² ]

=5(x-y-4z)(x-y+4z)
 

Answer 2

Bài 1:

a) x³-x+3x²y+3xy²+y³-y

=x³+2x²y-x²+xy²-xy+x²y+2xy²-xy+y³-y²+x²+2xy-x+y²-y

=x(x²+2xy-x+y²-y)+y(x²+2xy-x+y²-y)+(x²+2xy-x+y²-y)

=(x²+2xy-x+y²-y)(x+y+1)

=[x(x+y-1)+y(x+y-1)](x+y+1)

=(x+y-1)(x+y)(x+y+1) 

c) 5x²-10xy+5y²-20z²

=-5(2xy-y²+4z²-2)

Bài 2:

5x(x-1)=x-1   

=>5x²-6x+1=0

=>5x²-x-5x+1

=>x(5x-1)-(5x-1)

=>(x-1)(5x-1)=0

=>x=1 hoặc x=1/5

b) 2(x+5)-x²-5x=0

=>2(x+5)-x(x+5)=0

=>(2-x)(x+5)=0

=>x=2 hoặc x=-5