Solve {l}{x^2y^2-x^3}{-xy^2+x}

$$\left. \begin{array} { l } { x ^ { 2 } y ^ { 2 } - x ^ { 3 } } \\ { - x y ^ { 2 } + x } \end{array} \right.$$

Factor

$$x\left(1-x\right)\left(x-y^{2}+1\right)$$

Solution Steps

Factor out x.

$$x\left(xy^{2}-x^{2}-y^{2}+1\right)$$

Consider xy^{2}-x^{2}-y^{2}+1. Consider xy^{2}-x^{2}-y^{2}+1 as a polynomial over variable x.

$$-x^{2}+y^{2}x-y^{2}+1$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power -x^{2} and n divides the constant factor -y^{2}+1. One such factor is -x+1. Factor the polynomial by dividing it by this factor.

$$\left(-x+1\right)\left(x-y^{2}+1\right)$$

Rewrite the complete factored expression.

$$x\left(-x+1\right)\left(x-y^{2}+1\right)$$

Evaluate

$$x\left(1-x\right)\left(x-y^{2}+1\right)$$