a, = x3 - x2 + x2 - x + 5x - 5
= x2.(x-1) +x.(x-1)+5.(x-1)
= (x-1).(x2 + x +5)
b,=x.(x2 - 6x +9)
= x.(x2 -2.3.x +32)=x.(x-3)2
c, = (x^2 -y^2 ) -(x-y) = (x-y).(x+y)-(x-y)=(x-y).(x+y-1)
a)
\(x^3+4x-5\\ =x^3-x+5x-5\\ =\left(x-1\right)x\left(x+1\right)+5\left(x-1\right)\\ =\left(x-5\right)\left(x^2+x+5\right)\)
b)
\(x^3-6x^2+9x\\ =x^3-3x^2-3x^2+9x\\ =x^2\left(x-3\right)-3x\left(x-3\right)\\ =\left(x-3\right)\left(x^2-3x\right)\\ =\left(x-3\right)^2.x\)
c)
\(x^2-y^2-x+y\\ =\left(x-y\right)\left(x+y\right)-\left(x-y\right)\\ =\left(x-y\right)\left(x+y-1\right)\)