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\(x^3-2x^2-x\)
\(=x\cdot x^2-x\cdot2x-x\cdot1\)
\(=x\left(x^2-2x-1\right)\)

a) x2 + xy - 5x - 5y
=x(x+y)-5(x+y)
=(x-5)(x+y)
b) x2 - y2 - 4x + 4
=(x2-4x+4)-y2
=(x-2)2-y2
=(x-2-y)(x-2+y)
a) x2 + xy - 5x - 5y
= x ( x + y ) - 5 ( x + y )
= ( x + y ) ( x - 5 )
b) x2 - y2 - 4x + 4
= ( x2 - 4x + 4 ) - y2
= ( x - 2 )2 - y2
= ( x - 2 + y ) ( x - 2 - y )

\(x^8+3x^4+4\)
\(=\left(x^8-x^6+2x^4\right)+\left(x^6-x^4+2x^2\right)+\left(2x^4-2x^2+4\right)\)
\(=x^4\left(x^4-x^2+2\right)+x^2\left(x^4-x^2+2\right)+2\left(x^4-x^2+2\right)\)
\(=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)
\(4x^4+4x^3+5x^2+2x+1\)
\(=\left(4x^4+2x^3+2x^2\right)+\left(2x^3+x^2+x\right)+\left(2x^2+x+1\right)\)
\(=2x^2\left(2x^2+x+1\right)+x\left(2x^2+x+1\right)+\left(2x^2+x+1\right)\)
\(=\left(2x^2+x+1\right)^2\)

a/ x4 +5x3 +10x-4
=(x4- 4)+(5x3 + 10x)
=(x2+2) (x2-2) + 5x(x2 +2 )
=(x2+2)(x2 -2 +5x)
b/x5 - x4 +x3 -x2 +x-1
=x4(x-1)+x3(x-1)+(x-1)
=(x-1)(x4+x3+1)
`5x^2 + 5xy +x +y`
`=(5x^2 + 5xy )+(x+y)`
`=5x(x+y)+(x+y)`
`=(x+y)(5x+1)`
\(5x^2+5xy+x+y\\ =5x\left(x+y\right)+\left(x+y\right)\\ =\left(x+y\right)\left(5x+1\right)\)