Solve 3x^3+6x^2y-45xy^2

$$3 x ^ { 3 } + 6 x ^ { 2 } y - 45 x y ^ { 2 }$$

Factor

$$3x\left(x-3y\right)\left(x+5y\right)$$

Solution Steps

Factor out 3.

$$3\left(x^{3}+2x^{2}y-15xy^{2}\right)$$

Consider x^{3}+2x^{2}y-15xy^{2}. Factor out x.

$$x\left(x^{2}+2xy-15y^{2}\right)$$

Consider x^{2}+2xy-15y^{2}. Consider x^{2}+2xy-15y^{2} as a polynomial over variable x.

$$x^{2}+2yx-15y^{2}$$

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 -15y^{2}. One such factor is x+5y. Factor the polynomial by dividing it by this factor.

$$\left(x+5y\right)\left(x-3y\right)$$

Rewrite the complete factored expression.

$$3x\left(x+5y\right)\left(x-3y\right)$$

Evaluate

$$3x\left(x-3y\right)\left(x+5y\right)$$