a) $x^3-2x^2+x-xy^2$
$=x(x^2-2x+1-y^2)$
$=x[(x-1)^2-y^2]$
$=x(x-y-1)(x+y-1)$
b) $-5x^2+6x-1=-5x^2+5x+x-1$
$=(x-1).(-5x)+(x-1)$
$=(x-1)(-5x+1)$
c) $x^2y^2+1-x^2-y^2$
$=x^2y^2-x^2-(y^2-1)$
$=x^2(y^2-1)-(y^2-1)$
$=(x^2-1)(y^2-1)=(x-1)(x+1)(y-1)(y+1)$
d) $2x^2+3x-5$
$=2x^2-2x+5x-5$
$=2x(x-1)+5(x-1)=(2x+5)(x-1)$
a) \(x^3-2x^2+x-xy^2\)
\(=x\left(x^2-2x+1-y^2\right)\)
\(=x\left[\left(x-1\right)^2-y^2\right]\)
\(=x\left(x-1-y\right)\left(x-1+y\right)\)
b) \(-5x^2+6x-1\)
\(=-\left(5x^2-6x+1\right)\)
\(=-\left(5x^2-5x-x+1\right)\)
\(=-\left[5x\left(x-1\right)-\left(x-1\right)\right]\)
\(=-\left(x-1\right)\left(5x-1\right)\)
c) \(x^2y^2+1-x^2-y^2\)
\(=x^2y^2+2xy+1-x^2-2xy-y^2\)
\(=\left(xy+1\right)^2-\left(x+y\right)^2\)
\(=\left(xy+1-x-y\right)\left(xy+1+x+y\right)\)
\(=\left[x\left(y-1\right)-\left(y-1\right)\right]\left[x\left(y+1\right)+\left(y+1\right)\right]\)
\(=\left(y-1\right)\left(x-1\right)\left(y+1\right)\left(x+1\right)\)
d) \(2x^2+3x-5\)
\(=2x^2+5x-2x-5\)
\(=x\left(2x+5\right)-\left(2x+5\right)\)
\(=\left(2x+5\right)\left(x-1\right)\)
