Bài 1 : Phan tích đa thức thành nhân tử
a) x4 - 2x2 + 1
b) x2 - y2 - 5x + 5y
c) 2x3 - x2 - 8x + 4
d) x ( x - y )2 + y ( x - y )2 - xy + x2
e) 2x2 - 5x + 2
Bài 2 : Thực hiện phép tính chia
a) ( x3 + 6x2 + 8x - 3) : ( x2 + 3x - 8)
b) ( 2x4 - 7x3 + 9x2 - 7x + 2 ) : ( 2x2 - 5x + 2)
c) ( 2x2 + 4x2 + 5x + 10 ) : ( 2x2 + 5 )
d) ( x3 + 2x2 - 1 ) : ( 2x2 + x + 1 )
a) \(x^4-2x^2+1=\left(x^2-1\right)^2=\left(x-1\right)^2\left(x+1\right)^2\)
b) \(x^2-y^2-5x+5y=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x-y\right)\left(x+y-5\right)\)
c) \(2x^3-x^2-8x+4\)
\(=x^2\left(2x-1\right)-4\left(2x-1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(2x-1\right)\)
d) \(x\left(x-y\right)^2+y\left(x-y\right)^2-xy+x^2\)
\(=\left(x+y\right)\left(x-y\right)^2+x\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2-y^2+x\right)\)
e) \(2x^2-5x+2\)
\(=\left(2x^2-x\right)-\left(4x-2\right)\)
\(=x\left(2x-1\right)-2\left(2x-1\right)\)
\(=\left(x-2\right)\left(2x-1\right)\)