Solve x^5+9x^4y-10x^3y^2

$$x ^ { 5 } + 9 x ^ { 4 } y - 10 x ^ { 3 } y ^ { 2 }$$

Factor

$$\left(x-y\right)\left(x+10y\right)x^{3}$$

Solution Steps

Factor out x^{3}.

$$x^{3}\left(x^{2}+9xy-10y^{2}\right)$$

Consider x^{2}+9xy-10y^{2}. Consider x^{2}+9xy-10y^{2} as a polynomial over variable x.

$$x^{2}+9yx-10y^{2}$$

Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{2} and m divides the constant factor -10y^{2}. One such factor is x+10y. Factor the polynomial by dividing it by this factor.

$$\left(x+10y\right)\left(x-y\right)$$

Rewrite the complete factored expression.

$$x^{3}\left(x+10y\right)\left(x-y\right)$$

Evaluate

$$\left(x-y\right)\left(x+10y\right)x^{3}$$